Chapter 13.1, Problem 4AYU

To determine

To write: Whether the following statement is true or false. If $A$ is a set, the compliment of $A$ is the set of all the elements in the universal set that are not in $A$.

Answer to Problem 4AYU

True.

Explanation of Solution

Given:

Consider a set $A$.

Consider the universal set $U$. The elements of $U$ are either in $A$ or $A^{\prime }$.

Hence the “If $A$ is a set, the compliment of $A$ is the set of all the elements in the universal set that are not in $A$.” is true.