Chapter 3.5, Problem 5STP

For Exercises $1-6,$ choose the correct letter.

Suppose the universal set $U$ is the set of all real numbers and $M$ is the set of all real numbers greater than or equal to 8. Which number is not in $M^{\prime }?$

A. -8 B. 0 C. 5 D. 8

To determine

If $\left(U\right)$ is the universal set and $\left(M\right)$ is the set of all real numbers greater than or equal to 8 then find the number which is not in $\left(M\text{'}\right)$ .

Answer to Problem 5STP

The number 8 is not in set $\left(M\text{'}\right)$ , therefore option (D) is correct.

Explanation of Solution

Given information: It is given that $\left(U\right)$ is the universal set and $\left(M\right)$ is the set of all real numbers greater than or equal to 8.

Calculation: The set $\left(U\right)$ , $\left(M\right)$ and $\left(M\text{'}\right)$ for the given conditions is written as,

  $\begin{array}{c}U=\left\{R|R\text{is real}\right\}\\ M=\left\{R|R\text{}\text{ is real and }R\ge 8\right\}\\ M\text{'}=\left\{R|\text{}R\text{is real and }R<8\right\}\end{array}$

Since the set $\left(M\text{'}\right)$ represents the set of real numbers such that each real is less than 8 but we need the real number in $\left(M\text{'}\right)$ which is not in $\left(M\text{'}\right)$ . So the only number will be greater than or equal to 8. Now from options the only option (D) this condition. Therefore 8 is not in set $\left(M\text{'}\right)$ , therefore option (D) is correct.