AMSCO'S Geometry. New York - Rye High School

86 Logic•A hypothesis, also called a premise or antecedent, is an assertion thatbegins an argument. The hypothesis usually follows the word if.•A conclusion, also called a consequent, is an ending or a sentence thatcloses an argument. The conclusion usually follows the word then.• Beginning with a statement (p → q), the inverse (p → q) is formed bynegating the hypothesis and negating the conclusion.• Beginning with a statement (p → q), the converse (q → p) is formed byinterchanging the hypothesis and the conclusion.• Beginning with a conditional (p → q), the contrapositive (q → p) isformed by negating both the hypothesis and the conclusion, and theninterchanging the resulting negation.• Two statements are logically equivalent––or logical equivalents––if theyalways have the same truth value.•A biconditional (p ↔ q) is a compound statement formed by the conjunctionof the conditional p → q and its converse q → p.•A valid argument uses a series of statements called premises that haveknown truth values to arrive at a conclusion.LogicStatementsNegation: p not pConjunction: p ∧ q p and qDisjunction: p ∨ q p or qConditional: p → q if p then qInverse: p → q if p then qConverse: q → p if q then pContrapositive: q → p if q then pBiconditional: p ↔ q p if and only if qThe truth values of the logic connectives can be summarized as follows:NegationConjunctionDisjunctionConditionalInverseConverseContrapositiveBiconditionalp q p q p ∧ q p ∨ q p → q p → q q → p q → p p ↔ qT T F F T T T T T T TT F F T F T F T T F FF T T F F T T F F T FF F T T F F T T T T T