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) | |