2.1.2 Conditional Statements Key Objectives

• Identify, write, and analyze the truth value of conditional statements. • Write the inverse, converse, and contrapositive of a conditional statement. Key Terms • A conditional statement is a statement that can be written in the form “if p , then q .” • The hypothesis is the part p of a conditional statement following the word if . • The conclusion is the part q of a conditional statement following the word then . • A conditional statement has a truth value of either true (T) or false (F). • The negation of a statement p is “not p ,” written as ~ p .

• The converse is the statement formed by exchanging the hypothesis and conclusion. • The inverse is the statement formed by negating the hypothesis and conclusion. • The contrapositive is the statement formed by both exchanging and negating the hypothesis and conclusion. • Related conditional statements that have the same truth value are called logically equivalent statements . Theorems, Postulates, Corollaries, and Properties • Law of Contrapositive A conditional and its contrapositive are logically equivalent. Example 1 Identifying the Parts of a Conditional Statement A conditional statement is a statement that can be written in the form “if p , then q ,” where p is called the hypothesis and q is called the conclusion. If a statement or conjecture does not include the words “if” and “then,” the statement can be rewritten as a conditional statement by rephrasing and adding “if” and “then.”

Remember, the hypothesis of a conditional statement is the part that follows “if” and the conclusion of a conditional statement is the part that follows “then.” The first conditional given here is written in “if/ then” form, so the hypothesis and conclusion are easily identified. The second statement given here is not written in “if/then” form, but it does include the word “if.” So, rephrase the statement so that the part that follows “if” comes first and add the word “then” before the new second part.

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