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Pre-cal Logic
Flash Cards for Mrs. Wag's Logic Chapter
| Question | Answer |
|---|---|
| Mathematical Logic | symbolic, Bertrand Russel & A. N. Whitehead (England Principia Mathematica) |
| Statement | a sentence that states a fact or contains a complete idea. Can be judged T or F. |
| Negation | ~ results in opposite truth values |
| Quantifiers | some, all, one, none |
| ~ Some | “for some p” > “for all not p” |
| ~ All | “for all p” > “for some not p” |
| Conjunction | p^q. 2 statements connected by “and” |
| Disjunction | pvq. 2 statements connected by “or” |
| Conditional/Implication | p > q. |
| Converse | q > p. |
| Biconditional | whenever both the conditional and converse are T, p and q have = T values. |
| Tautology | compound statement that is always T regardless of the T values of its components. the biconditional of 2 = statements. |
| Logically Equivalent | 2 statements that have the same T values. |
| Inverse | ~p > ~q |
| Contrapositive | ~q > ~p |
| Law of Detachment (def) | if a conditional is T and its hypothesis is T, then its conclusion must be T |
| Law of Modus Tollens (def) | if a conditional is T and its conclusion is F, then its hypothesis is F |
| Law of Contrapositive (def) | if a conditional is T then its contrapositive is T |
| Law of Syllogism (def) | if 2 given conditionals are T a 3rd using the hypothesis of the 1st and the conclusion of the 2nd is T |
| Law of Disjunctive Inference (def) | if a disjunction is T and one of the disjuncts is F, then the other disjunct is T |
| Law of Disjunctive Addition (def) | if a given statement is T then a disjunction involving that statement and any 2nd statement is T |
| Law of Simplification (def) | if a conjunction is T then each of the conjuncts is T |
| Law of Conjunction (def) | if two statements are T, the conjunction is T |
| Negation of Conjunction (def) | the negation of a conjunction = the disjunction of the negation of each statement |
| Negation of Disjunction (def) | the negation of a disjunction of two statements = the conjunction of the negation of each statement |
| Law of Double Negation (def) | the negation of the negation statement is = to the statement |
| Invalid Reasoning (Asserting the Conclusion) | if a conditional is T and its conclusion is T then its hypothesis is not necessarily T |
| Invalid Reasoning (Denying the Premise) | if a conditional is T and its hypothesis is false then its conclusion is not necessarily F. |
| Law of Contrapositive (argument) | |
| Law of Detachment (argument) | |
| Law of Modus Tollens (argument) | |
| Law of Syllogism (argument) | |
| Law of Disjunctive Inference (argument) | |
| Law of Disjunctive Addition (argument) | |
| Law of Simplification (argument) | |
| Law of Conjunction (argument) | |
| Law of Double Negation (argument) | |
| Negation of a Conjunction (argument) | |
| Negation of a Disjunction (argument) | |
| Invalid Reasoning, Asserting the Conclusion (argument) | |
| Invalid Reasoning, Denying the Premise (argument) |
Created by:
YellowDucks
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