Chapter 3.5, Problem 7LC

To determine

To find: a nonempty set $A$ and $B$ is a set that contain at least one element, and suppose that $A\subseteq B$ , $B\subseteq A$ is always, sometimes or never true.

Answer to Problem 7LC

Sometime $A$ is a subset of $B$ ; sometimes $B$ is also a subset of $A$ .

Explanation of Solution

Given information:

The nonempty sets $A$ and $B$ .

Calculation:

Consider the nonempty sets $A$ and $B$ .

If $A$ is a subset of $B,A\subseteq B$ each element of $A$ is also an element of $B$ .

If $B$ is a subset of $A,B\subseteq A$ each element of $B$ is also an element of $A$ .

Both the conditions happen only when the elements of $A$ are equal to the elements of $B$ .

So, when $A$ and $B$ are equal sets.

Therefore, sometime $A$ is a subset of $B$ ; sometimes $B$ is also a subset of $A$ .