1. 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.

2. 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

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.
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.

4. 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

5. 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.