MATH-UA 121 Lecture Notes - Lecture 5: Sentence Clause Structure, Contraposition

• School: New York University
• Department: Math
• Course: MATH-UA 121
• Professor: Niu Xiaodong

Document Summary

Negation - (~) the opposite of a statement; the negation would cancel out the original statement. (^) the combination or multiple statements; basically means & . Conditional - (p q) a compound sentence that is formed by connecting two simple statements using the words ifthen . Converse - (q p) interchanging the hypothesis and the conclusion of the original conditional. Inverse - (~p ~q) denying both the hypothesis and the conclusion of the original conditional. Contrapositive - (~q ~p) interchanging the hypothesis and the conclusion then denying both of them from the original conditional. Bioconditional - (p > q) or [(p q) ^ (q p) if and only if p q conj disjunc condition convers. Contra+ biocond p ^ q p v q p q q p. ~q ~p p > q or (p-- Law of detachment (for conditionals!) p q p q . Law of contrapositive (only shows contrapositives!) p q.