Chapter 2, Problem 1T

To determine

The union of the sets A and C, that is $A \cup C$

Answer to Problem 1T

Solution: $\underset{\_}{\left\{a,b,c,d,e\right\}}$

Explanation of Solution

Given:

The sets as

$U=\left\{a,b,c,d,e,f,g,h\right\},A=\left\{a,b,c,d\right\},B=\left\{b,e,a,d\right\}\text{ and }C=\left\{e,a\right\}$

Explanation:

The elements of the set $A$ are $\text{a,}\text{b,}\text{c,}\text{and}\text{d}\text{.}$

The elements of the set $C$ are $\text{e}\text{and}\text{a}\text{.}$

$A \cup C$ denotes the union of the sets $A \text{and}C.$

Therefore, the elements that are in $A$ or in $C$ or in both $A$ and $C$ are $\text{a,}\text{b,}\text{c,}\text{d}\text{and}\text{e}\text{.}$

$\text{i}\text{.e}\text{.,}A \cup C=\left\{\text{a,}\text{b,}\text{c,}\text{d}\right\}\cup \left\{\text{e,}\text{a}\right\}=\left\{\text{a,}\text{b,}\text{c,}\text{d,}\text{e}\right\}$

Hence, $A \cup C=\left\{\text{a,}\text{b,}\text{c,}\text{d,}\text{e}\right\}$