Chapter 0, Problem 1RE

To determine

If $A\subseteq B$

where $A=\left\{1,2,5,7\right\}$ and $B=\left\{x:x\text{and is a positive integer,}x\le \text{8}\right\}$.

Answer to Problem 1RE

Solution:

The answer is yes, $A\subseteq B$.

Explanation of Solution

Given Information:

The given sets are $A=\left\{1,2,5,7\right\}$

and $B=\left\{x:x\text{and is a positive integer,}x\le \text{8}\right\}$.

Explanation:

Let us convert the set B in another form.

$B=\left\{1,2,3,4,\text{}5,6,7,8\right\}$

We see that every element of A is an element of B.

So, $\left\{1,2,5,7\right\}\subset \left\{1,2,3,4,\text{}5,6,7,8\right\}$

Therefore, $A\subseteq B$.