Chapter B, Problem 2YT

To determine

Whether the statement “$\left\{8,9,10\right\}\subseteq \left\{8,9\right\}$” is true or false.

Answer to Problem 2YT

Solution:

The statement “$\left\{8,9,10\right\}\subseteq \left\{8,9\right\}$” is false.

Explanation of Solution

Given Information:

The statement is “$\left\{8,9,10\right\}\subseteq \left\{8,9\right\}$”.

Consider the statement.

$\left\{8,9,10\right\}\subseteq \left\{8,9\right\}$

Suppose every element of A is an element of B, then A is a subset of B is:

$A\subseteq B$

In the given set $10\in \left\{8,9,10\right\}$ but $10\notin \left\{8,9\right\}$.

Thus, $\left\{8,9,10\right\}\subseteq \left\{8,9\right\}$ is not true.

Therefore, the statement $\left\{8,9,10\right\}\subseteq \left\{8,9\right\}$ is false.