College Math

College Math Study Guide

6.7 Conditional Statements Conditional statements are denoted by an arrow sign →, and are of the form “if a then b”. It is written as a → b In this case, a is known as an antecedent and b is termed as the consequent of the conditional statement. The truth value table for conditional statements is given here: a b a → b T T T T F F F T T F F T 6.8 Logical Equivalence Two statements are logically equivalent when their truth values are identical. For instance, two compound statements denoted by a → b and (~ a) ∨ b show logical equivalence, as shown in the following truth table: a b a → b ~ a (~ a) ∨ b T T T F T T F F F F F T T T T F F T T T Let us take an instance for logical equivalence. a = If the book is a good value, I will buy it b = The book is a good value or I will buy it Both these statements have logical equivalence.

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