Q68. - Algebra 2

Question

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

 

Every real number is a rational number. 

Step-by-Step Solution

Answer

The statement is false.

Step 1- Apply the concept of real number.

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

Step 2- Step description.

A rational number is a number that is of the form $\frac{p}{q}$ where $p$ and $q$ are integer and $q$ is not equal to 0.

 

Let a real number $\sqrt{11}$ that is irrational but not rational.

Step 3- Step description.

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

 

Therefore, the statement is false.