Chapter 1.1, Problem 44E

(a)

To determine

To find: the set $A\cap C$ .

Answer to Problem 44E

  $A\cap C=\left\{x|-2\le x\le 5\right\}$

Explanation of Solution

Given information:

Three sets are givenas $A=\left\{x|x\ge -2\right\},B=\left\{x|x<4\right\}$ , and $C=\left\{x|-1<x\le 5\right\}$

Formula used:

For any two or more sets, intersection of the sets gives the elements which are the only common elements of the sets. Intersection is represented by the symbol $\cap$ .

Calculation:

Consider the given sets.

  $A=\left\{x|x\ge -2\right\}$

and

  $C=\left\{x|-1<x\le 5\right\}$

Now, $A\cap C$ will contains common elements of A and C.

  $\begin{array}{c}A\cap C=\left\{x|x\ge -2\right\}\cap \left\{x|-1<x\le 5\right\}\\ =\left\{x|-2\le x\le 5\right\}\end{array}$

(b)

To determine

To find: the set $A\cap B$ .

Answer to Problem 44E

  $A\cap B=\left\{x|-2\le x<4\right\}$

Explanation of Solution

Given information:

Three sets are given as $A=\left\{x|x\ge -2\right\},B=\left\{x|x<4\right\}$ , and $C=\left\{x|-1<x\le 5\right\}$

Formula used:

For any two or more sets, intersection of the sets gives the elements which are the only common elements of the sets. Intersection is represented by the symbol $\cap$ .

Calculation:

Consider the given sets.

and

  $B=\left\{x|x<4\right\}$

Now, $A\cap B$ will contains common elements of B and A.

  $\begin{array}{c}A\cap B=\left\{x|x\ge -2\right\}\cap \left\{x|x<4\right\}\\ =\left\{x|-2\le x<4\right\}\end{array}$