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Chapter 1: Q68. (page 32)

Determine whether each statement is true or false. If false, give a counterexample.

Every real number is a rational number.

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Step 1- Apply the concept of real number.

Real numbers are simply the combinations of rational and irrational numbers.

02

Step 2- Step description.

A rational number is anumberthat is of the form pq where p and q are integer and q is not equal to 0.

Let a real number 11 that is irrational but not rational.

03

Step 3- Step description.

Sincereal number contains the combination of rational and irrational numbers thus the statement is false.

Therefore, the statement is false.

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