 # EXAMPLE 5 Rewrite a conditional statement in if-then form

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EXAMPLE 5 Rewrite a conditional statement in if-then form Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. SOLUTION a. Given: No integers are irrational numbers. If-then form: If a number is an integer, then it is not an irrational number. The statement is true.

EXAMPLE 5 Rewrite a conditional statement in if-then form b. Given: All real numbers are rational numbers. If-then form: If a number is a real number, then it is a rational number. The statement is false. For example, is a real number but not a rational number. 2

EXAMPLE 5 GUIDED PRACTICE Rewrite a conditional statement in if-then form for Example 5 Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. All square roots of perfect squares are rational numbers. 10. If-then form: If a number is the square root of perfect square, then it is a rational number. The statement is true.

EXAMPLE 5 GUIDED PRACTICE Rewrite a conditional statement in if-then form for Example 5 Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. All repeating decimals are irrational numbers. 11. If-then form: If a number is a repeating decimal, then it is an irrational number. The statement is false. For example, 0.333… is a repeating decimal and can be written as , so it is a rational number. 1 3

EXAMPLE 5 GUIDED PRACTICE Rewrite a conditional statement in if-then form for Example 5 Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. No integers are irrational numbers. 12. If-then form: If a number is an integer, then it is not an irrational number. The statement is true.