Critical Thinking Pdf Notes Basic Computer

Critical Thinking- Week 1 Notes What is Critical Thinking? • Critical thinking is about evaluating beliefs. • Critical thinking is not about where your beliefs come from. • Sociology and psychology study why we believe what we believe. • It’s about which beliefs are worth having. • We assume a belief is worth having provided it’s most likely true. • We also assume a belief is most likely true if there are good reasons to accept it. “Critical thinking is the systematic evaluation or formulation of beliefs, or statements, by rational standards.” • It’s systematic because it involves distinct procedures and methods (not just gut feelings). • It’s used to evaluate existing beliefs and formulate new ones. • It evaluates beliefs in terms of how well they are supported by reasons. We Should Think Critically Because:  Who we are is determined largely because of our actions and choices  Our actions and choices are in turn determined by our thoughts and beliefs  If we don’t choose our beliefs carefully were giving up control. Critical Thinking is all about thinking OUTSIDE of the box:  Its about challenging our assumptions  Asking hard questions  Rejecting biases, stereotypes, and other unreasonable assumptions To Think Critically you need to be able to think, listen, and read slowly and attentively. It helps you understand a few definitions and concepts. DEFINITIONS: Assertion (statement) : An Assertion is a declarative sentence that is intended to make a claim of some sort. Sometimes these are called statements or propositions. “Im taller than you” “it is raining” “she will win the race.” Not all sentences are declarative. Questions are not assertions. Premise: A statement offered in support of a conclusion. Conclusion: A conclusion is a statement that is held to by supported by a premise or premises. Premise: All Whales are mammals Premise: Moby Dick is a whale Conclusion: Moby Dick is a Mammal. Argument An argument is a set of statements one of which (the conclusion) is taken to be supported by the remaining statements (the premises). Here’s another way of saying this: • An argument is a group of statements in which some (the premises) are intended to support another (the conclusion). • The conclusion is what the speaker wants you to accept. • The premises state the reasons or evidence for accepting the conclusion. • An argument must have a conclusion; the idea of what is the claim in the passage that an individual is trying to persuade you of. • Typical argument will have mini claims to support it. Inference: An inference is the move from a premise (or premises) to a conclusion (or conclusions). • Critical thinking is all about inferences. • Inferences are identified and evaluated. Explanation and Argument should not be confused.  An explanation tells you why something happened  An argument tells you why you should believe something, an argument tries to persuade you.  Arguments have something to prove; explanations do not Example; 1. Adam stole the money, for three people saw him do it 2. Adam stole the money because he needed it to buy food Not all statements contain arguments:  To recognize arguments look for a conclusion and look for a premises.  These can often be identified by certain indicator words such as: Conclusion- Indicators  Thus  Therefore  Hence  Entail(s)  … it follows that …  … we may conclude …  Consequently  So Premise- Indicators • Since • Because • For • As • … given that … • … inasmuch as … • … for the reason that … Two Points About Indicator Words First: They may not actually be present in arguments. Second: In arguments, premises do not always come before conclusions; conclusions do not always come after premises “textual priority versus logical priority.” “Religious beliefs cannot be proven. If something is a matter of faith, it cannot be proven, and religious beliefs are obviously a matter of faith.” Truth Versus Logical Strength; • Premises and conclusions may be true, or they may be false. • Evaluating the truth-value of premises and conclusions is distinct from evaluating the logical strength of arguments. (1) Ryerson University is in Guelph, ON. (2) The RAC is located within Ryerson U. ___________________________ Therefore, 3) The RAC is located in Guelph, ON. Validity and Soundness. Deductive Validity: An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false. i.e., if all the premises were true, the conclusion would have to be true too. An argument is deductively invalid if and only if it is not deductively valid. A deductively valid argument: (1) All bachelors are unmarried. (2) Ivan is a bachelor. ____________________________ Therefore, (3) Ivan is unmarried. Note: This is a special use of the word ‘valid’ Remember, a valid argument need not have true premises, and it need not have true conclusions: what’s important is the logical relationship between the premise(s) and conclusion(s). (1) All Americans are ten feet tall. (2) Prof. Hunter is an American . Therefore, (3) Prof. Hunter is ten feet tall Two False Premises and False Conclusion. Deductive Soundness: An argument is deductively sound if and only if it is deductively valid and all its premises are true. Deductive Versus Inductive Arguments In a deductively valid argument, the truth of the premise(s) guarantees the truth of the conclusion(s). But, not all arguments are deductive: Inductive Strength: An argument is inductively strong if and only if the conclusion is probably true, given the premises. An argument is inductively weak if and only if it is not inductively strong. ***** In the case of any argument the point is not whether the premises/conclusions are actually true or false, its weather supposing that the premises were true they would guarantee that the conclusion is true too. If they would the argument is valid. Inductively Strong Argument: (1) Quitting smoking usually improves your health. (2) Mary has quit smoking. Therefore, probably (3) Mary’s health will improve. Inductively Weak Argument: (1) A few police officers are corrupt. (2) Jim is a police officer. Therefore, probably, (3) Jim is corrupt. Critical Thinking- Week Two Notes:  Impediments to CT Critical Thinking is the systematic evaluation or formulation of beliefs or statements by rational standards. Common Impediments to Critical Thinking: Category 1: Hindrances that arise because of how we think Category 2: Hindrances that occur because of what we think. Category 1 impediments to Critical Thinking (a) Self- interested thinking: Accepting a claim SOLELY on the grounds that it advances or coincides with our interests. Overcoming Self- Interested Thinking:  Watch out when things get very personal  Be alert to ways that critical thinking can be undermined( ex; wishful thinking)  Ensure that nothing has been left out  Avoid Selective Attention  Look for Opposing evidence. (B) Group Thinking: Peer Pressure  Fallacy: An argument form that is both common and defective.  Fallacy of appeal to popularity  Fallacy of appeal to common practice  Fallacy of appeal to tradition  Genetic Fallacy. Stereotyping: Drawing conclusions about people or groups without sufficient reasons. Some Terminology Concerning Knowledge:  Knowledge has to be beliefs that are true.  Different uses of “knowledge.”  Knowledge by acquaintances  Knowledge- how  propositional Critical Thinking- Week 3 Notes – Chapter 1 & 2 quiz next week.  Follow study guide for quiz next week, things that are not on the study guide, are not on the quiz.  Study guide covers his slides and the textbook.  Few passages will be given, and will be asked if its an argument if it’s an argument it will be asked to give the premises and conclusions. (Chapter 1).  I’ll be asked to explain category 1 and category 2 impediments.  Bring Pen! Deductive Argument: • A deductive argument is intended to provide conclusive support for its conclusion. • A deductive argument that succeeds in providing conclusive support for its conclusion is said to be valid. • One that fails to provide conclusive support is said to be invalid. • A valid argument is such that if its premises are true, then its conclusion must be true. • For this reason, deductively valid arguments are said to be truth-preserving. • Valid is same as truth preserving. • If the premises are truth the conclusion MUST be true. • Not all deductively valid arguments have true premises and true conclusions. • In fact, a valid argument may have any of the following combinations: • True premises and true conclusion • False premises and true conclusion • False premises and false conclusion • The only combination a valid argument may not have is true premises and false conclusion. • Explanation: if it’s a valid argument it must be truth preserving, if the premises are true the conclusion must be true. • A deductively valid argument with true premises is said to be sound. • Sound means argument is valid and all of the premises are TRUE. • A sound argument can have a false conclusion. FALSE statement. In fact, we don’t even need to know the truth-value of the premises and conclusions in order to know that an argument is valid. Consider: (1) Either Jones or Smith committed the murder. (2) Jones didn’t commit the murder. .: (3) Smith committed the murder.  Inspection of the logical structure of this argument, by itself, tells us that it is valid.  Our test for validity: suppose that the premises are all true. Then, ask yourself: supposing that the premises are true is it possible for the premises to be false? If it is not possible, the argument is valid.  Inductive argument would state what something probably would be the case.  Inductive arguments are never valid. (ii) Inductive Arguments 1. An inductive argument is intended to provide probable support for its conclusion. 2. An inductive argument that succeeds in providing probably support for its conclusion is said to be strong. A strong inductive argument is such that if its premises are true, its conclusion is probably true. 3. A strong inductive argument with true premises is said to be cogent. 4. Because the conclusion of an inductive argument is not guaranteed to be true by the truth of the premises, inductive arguments are not truth-preserving.  Cogent Means Strong- If the premise is true than the conclusion is probably true.  Cogent inductive argument can have a false conclusion - > False. Inductively Strong Argument: (1) Quitting smoking usually improves your (2) Mary has quit smoking. Therefore, probably (3) Mary’s health will improve. Inductively Weak Argument: (1) A few police officers are corrupt. (2) Jim is a police officer. Therefore, probably, (4) Jim is corrupt. health. Chapter Two The Environment of Critical Thinking: Impediments to CT: Impediments to critical thinking classified Recall our first definition: Critical thinking is the systematic evaluation or formulation of beliefs or statements by rational standards. Common impediments to critical thinking: Category 1: hindrances that arise because of how we think. Category 2: hindrances that occur because of what we think. Category 1 Impediments to Critical Thinking (a) Self-Interested thinking: accepting a claim solely on the grounds that it advances, or coincides with, our interests. Overcoming self-interested thinking:  Watch out when things get very personal.  Be alert to ways that critical thinking can be undermined (ex: wishful thinking).  Ensure that nothing has been left out:  Avoid selective attention.  Look for opposing evidence. (b) Group Thinking:  Peer pressure Fallacy: an argument form that is both common and defective.  Fallacy of appeal to popularity  Fallacy of appeal to common practice  Fallacy of appeal to tradition  Genetic fallacy  Stereotyping: drawing conclusions about people or without sufficient reasons. groups Some Terminology Concerning Knowledge. Different uses of “knowledge”:  Knowledge by acquaintance  Knowledge-how  Propositional knowledge (knowledge-that) Three key ingredients in Propositional knowledge:  Belief  Truth  Justification Referred to as Tri Partied conception of knowledge; Knowledge has these three parts. Our goal is to have a lot of knowledge, and have evidence that would support our claims. 5) Category 2 Impediments to Critical Thinking. Hindrances that occur because of our views about truth and knowledge.  Subjective Relativism.  Social Relativism.  Skepticism. If you do not believe there is an objective truth, than you are a relativist. Relativism: the view that intentions have a truth-value, but that what this is depends upon (i.e. is relative to) some person or social group. (i) Subjective Relativism The view that the truth-value of a proposition depends solely upon (is relative to) what some subject believes. “ that’s true for you “ “ that’s my truth” Objections: (a) This is unlikely: consider the jar of jelly beans (b) This view would make us (Infallible-> meaning you believe you cant make an error) (c) This view is self-defeating (i.e. if it’s true, then it is an example of a truth that is not relative). Subjective relativist is saying there is no absolute truth. (ii) Social Relativism The view that the truth-value of a proposition depends solely upon (is relative to) societies. It is talking about something more broad. Why might someone hold this view? Objections: (a) Implausible (b) Intolerant views (c) Would make societies infallible (infallible means you believe that you cannot make an error.) (c) Self-defeating. Philosophical Skepticism: o The view that propositions have truth-values, but that we know what very few, or none, of them are. o (In other words, we know a lot less than we think, or nothing at all.) Why Hold this View? (a) Dream Hypothesis (b) Evil Genius Hypothesis e.g. Machine hypothesis René Descartes (1596-1650) Consider the following argument for skepticism: (1) Unless I am completely certain that I am not being deceived by an evil genius, my beliefs lack justification (they do not count as knowledge). (2) I am not completely certain that I am not being deceived by an evil genius. Therefore, (3) My beliefs lack justification (they do not count as knowledge). Objection:  Requiring absolute certainty for a belief to count as knowledge is asking too much. Each category 2 impediments to critical thinking denies something about truth or knowledge: Relativism- subjective RelativisimNEXT STEPS:  Review Chapters 1 & 2: do the exercises in the textbook (pp.52-60). Feel free to skip the “Writing Exercises” on pp.61-63.  Go to the online study guide, and work though the exercises and interactive quizzes for Chapters 1 and 2 until you feel you have mastered the material.  Review Quiz #1 Study Guide (to be posted early next week).  Attend and participate in your one-hour tutorial. (On your weekly class schedule, you’ll see the word “lecture” in the onehour time-slot for SSH105. Don’t be misled: this is, in fact, your tutorial.) Memorize you section #. You will need to write this on your tests/exams!!! Critical Thinking Week 4: Lecture Topics: 1. Deductive Vs. Inductive Arguments 2. Deductive Argument Patterns 3. Diagramming Arguments. Conditional Statement: Conditional statement is a statement of the form If P, Then Q. Example:  If it rains the picnic will be cancelled  If Jones didn’t commit the murder the butler did.  Conditions are compound statements composed of two parts:   The Antecedent: What follows the word “if” The Consequent- What follows the word “then”  Conditional is a compound statement it is an If and Then Statement.  When doing a scheme of argument of abbreviation NEVER break up a conditional.. a Conditional is always saying one thing.  By Contrast a Conjunction is telling two things…. Ex; it rained and then the picnic was cancelled.   A Conditional is a promise. Ex; if you pass the course; Ill Buy you a donut. The Idea that if you meet a certain condition than someone will buy you a donut. Conditionals make a single assertion and that assertion is thought of as a promise or a guarantee. Disjunctive Statements:  A Disjunctive Statement is a statement of the form.  Either P or Q Examples;  Either the picnic was cancelled or it rained  Either Jones committed the murder or the butler did Disjunctions are compound statements composed of two parts called the disjuncts. Some Valid Conditional Argument Patters. 1. Affirming the Antecedent ( Modus Ponens): If P, then Q. P. Therefore, Q. Example; 1. The conservative won the election, then Stephen harper is the new prime minister. 2. The conservatives won the election. 3. Therefore, Stephen Harper is the new prime minster. Always in a conditional the antecedent expresses a sufficient condition Some Valid Conditional Argument Patterns. 3. Denying the Consequent( Modus Tollens) If P, Then Q. Not Q. Therefore, Not P Example; 1. If the liberals won the election, then Paul Martin is the new prime minister 2. Paul martin is not the new prime minister 3. Therefore, The liberals did not win the election. The consequent in a conditional always expresses what is a called a necessary condition.  Antecedent equal sufficient conditions for the consequence.  The consequent expresses a necessary condition Hyopothetical Syllogism If P, then Q. If Q, then R Therefore, if P then r. Example; (1): If the conservatives won the election, then stepher harper is the new Prime Minister. (2) If Stephen Harper is the new Prime Minister, then someone from Alberta I s the new prim minster (3) Therefore, if the conservatives won the election then someone from albera is the new prime minister. Denying the Antecedent: ( Invalid) If P, then Q. Not P Therefore, Not q. Example; If it’s a square it has 4 sides It isn’t a square Therefore, its not a square Example; If Einstein invented the computer, then he’s a genius Einstein did not invent the computer Therefore, he’s not a genius Affirming the Consequent ( Invalid) If p, then q Q, Therefore P A Valid Disjunctive Argument Pattern Disjunctive Syllogisms: Either P or Q Not P Therefore, Q. Either P or Q Not Q Therefore , P. Diagramming Arguments Before evaluating an argument, therefore it often helps to reconstruct it in a more perspicuous manner. One way make DIAGRAM of argument. Method for Diagramming Arguments: Step 1: Underline premise and indicator words Step 2: Find conclusion and draw line under It Step 3: Locate the premises and draw a line under them Step 4: Cross out statements, irrelevant sentences, questions, exclamations. Step 5: Draw the diagram. Critical Thinking- Week 6 Notes: Conditional statements and necessary conditions vs Sufficient Conditions “ A is necessary condition for B”, means “without A, B would not be true.” A” is a sufficient condition for B” Means “ If A is true, then B would have to be true as well.” (e.g) If john is a bachelor, then John is unmarried.   The Consequent- “John is unmarried”- expresses a necessary condition for its being true that John is a bachelor; If It was false than he could not possibly be a bachelor. But being unmarried is not sufficient for being a bachelor one must also be male. The Antecedent Condition- “John is a bachelor”- expresses a sufficient condition for its being true that John is unmarried. If it were true that John is a bachelor, then it would have to be true that he is unmarried. But being a bachelor is not necessary condition for being unmarried. Women are often unmarried, although they are never bachelors. Diagramming Arguments:  Before evaluating an argument, it often helps to reconstruct it in a more perspicuous manner. ONE way is to make a diagram of the argument. Step 1: Mark all the indicator words Step 2: Number all the assertions in the argument Step 3: Identify the main conclusion of the argument Step 4: identify the premises that directly support the conclusions Step 5: decide whether these are dependent or independent premises. Week 5: Critical Thinking Notes – Chapter 4- Reasons for Belief and Doubt: 1) When Claims Conflict 2) Experts and Evidence 3) Personal Experience 4) Fooling ourselves Reasons for Belief and Doubt  If we care whether our beliefs are true or reliable, then we must care about the reasons for accepting those beliefs. (1)When Claims Conflict  When two claims conflict, they simply cannot both be true  If a new claim conflicts with other claims we have good reason to accept, we have good grounds for doubting the new claim.  With conflicting claims, you are not justified in believing either one of them until you resolve the conflict.  Two types of conflict:  2 statements can be “inconsistent”- I.E. can’t both be true, but could both be false. E.G. “today is Monday” and “today is Wednesday” are inconsistent  2 statements can be contradictories- I.e. cant both be true, but(also) cant both be false. E.g. “there is a video of Rob Ford” and “ there is not a video of Rob Ford” are both Contradictories. Another Type of Conflict  Conflict with Background information  Sometimes rather than two conflicting claims we see a conflict between a claim and your “ background information.”  “background information’ includes:  Facts about everyday things  The sky is blue  Beliefs based on very good evidence  Cigarettes aren’t good for you  Justified claims that we would regard as common sense or common knowledge  If you study, then you will do better on the quiz. Example “ some babies can bench press 500 pounds  You are not going to be able to accept this claim because it conflicts with an enormous number of your background beliefs about physiology, gravity, and weight lifiting.         The more background information the claim conflicts with the more reason we have to doubt it. But, it is always possible; of course that a conflicting claim is true and some of our background information is unfounded. COMMON SENSE isn’t always RIGHT Many people believe: Shark attacks are common Flying in an airplane is dangerous SUVS are safer to own than smaller cars YET, these are all false. Beliefs and Evidence  We should proportion our belief to the evidence.  Our degree of belief should vary according to the evidence  The more evidence a claim has in favor, the stronger our belief in it should be.  It is not reasonable to believe a claim when there is no good reason for doing so  Believing shouldn’t be your default setting. (2)Experts and Evidence  When an unsupported claim doesn’t conflict with what we already know, we are often justified in beliefing it because it comes from experts.  If an expert makes a claim then we are more justified in believing it  Even if no evidence is given  So long as it doesn’t conflict with background information What is an expert? How does the textbook define it?  Expert defined is someone who has more knowledge.  Someone who is more knowledgeable in particular subjects than other people. What good is an expert?  In their specialty areas, experts are more likely to be right because:  They have access to more information on the subject  They are better at judging that information than we are  This is primarily because of their greater experience and practice  In a complex world people must rely on experts  You cant be a doctor And lawyer and mechanic… BUT good critical thinkers are careful about expert opinion. When to doubt a expert  If a claim conflicts with expert opinion, we have good reason to doubt it  Example: the earth is about 10,000 years old  When experts disagree over a claim we have good reason to withhold judgment. Have you found the right expert?  When a claim comes from someone deemed to be an expert who in fact is not an expert we commit the fallacy known as appear to authority  Here is one of the 2 ways appeal the authority can happen:  First just because someone is an expert in one field he or she is not necessarily an expert in another  The second way appeal to authority can happen is that.  We may fall into a fallacious appeal to authority by regarding a non expert as an expert  Movie stars, acts, and famous athletes. To be considered an expert:  Someone must have shown that he or she can assess relevant evidence and arguments and arrive at well supported conclusions in a particular field  A few indicators to consider someone an expert are  Amount of education and training  Experience in making reliable judgments  Professional Experience (3) Personal Experience  We accept a great many claims because they are based on personal experiences- our own or someone else’s  But can you trust personal experience to reveal the truth?  It is reasonable to accept the evidence provided by personal experience only if there’s no good reason to doubt it.  For examples  If we seem to see a cat on the mat under good viewing conditions, then we’re justified in believing that there’s a cat on the mat  But sometimes our attention is flawed.  Factors that can give us a good reason to doubt the reliability of personal experience  Impairment  Expectation  Innumeracy  Impairment  If our perceptual powers are somehow impaired, we have reason to doubt them  The following are reasons to doubt the trustworthiness…  …..  ….  Expectation We often perceive exactly what we expect, regardless of whether there’s really anything to detect. Innumerac Another common error is the misjudging of coincidences.. Another error is to think that previous events can affect the probabilities in the random event at hand E.g. The coin has turned up heads seven times in a row so its more likely that it will turn up tails the next flip This is example of Gamblers Fallacy The lessons here is not that we should mistrust all judgment about probabilities but rather that.. Fooling ourselves We too offent fail to give evidence its due We Ignore evidence Deny evidence There of the most common and most serious mistakes we are  Resisting contrary evidence  Looking only for confirming evidence  Preferring available evidence Resisting contrary evidence  We resist evidence that flies in the face of our cherished beliefs  This can be psychologically comforting but it can prevent any further search for knowledge  Often you will see evidence you want to see and be blind to what we don’t want to see. Looking only for confirming evidence  We often seek out and use only confirming evidence. This is known as confirming bias  The result we can end up accepting a claim that is now true Remember when we evaluate claims we should look for disconfirming and conforming evidence. Preferring available evidence Availabilit error: we rely on evidence because it is memorable or striking or rather because it is phsychologically available Note also if you ask people to visualize something they will tend to say that its common. Week 7- Critical Thinking: Why worry about Logical Structure? (1) Comprehension: Helps us to better see the underlying forms of arguments (2) Positive evaluation: Helps us to readily spot (and create) valid arguments (3) Negative Evaluation: Helps us to readily spot (and avoid creating )Invalid arguments Some Terminology: Simple Statement: Contains no other statement as a component part. (We represent it with a letter, like “P”.) Complex Statement: Contains at least one other statement as a component part. Logical Operator: Special expressions which work to combine simple statements into complex ones. Examples: Simple statements: Alice is happy (A) Jim is sad (J) Logical Operators: (1) Conjunction: Alice is happy AND Jim is sad A&J [Exercise: When is this statement false?] (2) Negation: Alice is not happy. not-A ~A [Exercise: When is this statement false?] 3) Disjunction: Alice is happy OR Jim is sad A or J AvJ [Exercise: When is this statement false?] (4) Conditional: IF Alice is happy, THEN Jim is sad. If A then J AàJ “antecedent” à “consequent” “à” is the implication operator [Exercise: When is this statement false?] As soon as you see a antecedent is false the conditional MUST be true.. ONLY time conditional is true when consequent is false. Spotting Logical Operators Just like premise- indicators logical operators are not always explicitly present in a text. (a) Conjunctions Paul Martin is a prime minister now, but Stephen harper will be soon The lecture was poorly- presented even though the topic was interesting Other conjuct words: however’, ‘although’, ‘nonetheless’, ‘moreover’. (2) Negations Other expressions include: ‘it’s not true that’; ‘it’s false that’; ‘it’s not the case that’. (3) Disjunctions English: ‘exclusive’ sense. “A v B, and not both.” Logic: ‘inclusive’ sense. “Sam will get a sunburn unless she applies lotion.” “unless” = “or” (4) Conditionals “Since your lease expired the landlord is free to raise the rent” “Being a teenager means you have lots of problems” “Anyone who likes logic is a fool” “The truth of evolution implies the falsity of the Bible” “Whenever Lebowski drinks coffee, he gets antsy” A (Slightly) Tricky Point About Conditionals: “If” vs “Only If” The word “if”, by itself, introduces the antecedent, no matter where it occurs in a statement. “If I skip class, I’ll find the material difficult” “I’ll find the material difficult if I skip class. These are equivalent, and should be written as: S à D The expression “only if” introduces the consequent, no matter where it occurs in a statement. “Only if the price drops will I buy the giant TV” “I will buy the giant TV only if the price drops” These are equivalent, and should be written as: B à P Another (Slightly) Tricky Point: Combining Logical Operators A logical operation can be performed on a compound statement: Both Tim and Sue will win the award. T & S It’s not the case that both Tim and Sue will win the award. ~ (T & S) Just like in math, it matters where you put the brackets: the sentence above is not equivalent to ~T & S Similarly, there’s an important difference between these two: R à (W & M) If it rains, I am wet and miserable. (R à W) & M If it rains, I am wet. And I’m miserable Combining Conjunction and Disjunction With Negation Consider a conjunction, which is then negated: Both Tim and Sue will graduate. It’s not the case that both Tim and Sue will graduate. T&S ~ (T & S) This is not equivalent to ~T & ~S Why? But it is equivalent to ~T v ~S Why? Next, consider a negated disjunction: ~ (T v S) This reads: It’s not the case that either Tim or Sue will graduate. This is not equivalent to ~T v ~S This is equivalent to ~T & ~S Why? Why? A truth-table sets out all possible truth-value assignments for a given complex statement, and its component simple statements. Negation flips the truth value.

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