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Chapter 2.2 Conditional Statements

DISCRETE MATH: LECTURE 3DR. DANIEL Conditional Statements Ifpandqare statement variables, theconditionalofqbypis Ifpthenq or pimpliesq and is denotedp q. It is false whenpis true andqis false; otherwiseit is true. We callpthehypothesis(orantecedent) of the Conditional andqtheconclusion(orconsequent).pqp qTTTFFTFF A Conditional statement that is true by virtue of the fact that its hypothesis is falseis calledvacuously trueortrue by default. In general, when the if part ofan if-then statement is false, the statement as a whole is said to be true, regardlessof whether the conclusion is true or example:If 0 = 1, then 1 = 2. NOTE: Theorder of operationsfor evaluating Statements is first, then and , and finally .For example:Construct the truth table for the statementp q p qp qp q Class Group Work:Show thatp q r (p r) (q r).

1. Chapter 2.2 Conditional Statements If p and q are statement variables, the conditional of q by p is "If p then q" or "p implies q" and is denoted p !q. It is false when p is true and q is false; otherwise it is true. We call p the hypothesis (or antecedent) of the conditional and q the conclusion (or consequent). p q p !q T T T F F T F F

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