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# Pre-cal Logic

### Flash Cards for Mrs. Wag's Logic Chapter

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)