Question

Find (a) the number of subsets and (b) the number of proper subsets of the set.{x 1 x is an even integer between - 3 and 3)(a) The given set has subsets.(Simplify your answer.)proper subsets(b) The given set has(Simplify your answer.)

Answer 1

The number of subsets follows the rule

$2^n$

Where n represents the number of elements inside the set.

The number of proper subsets is defined as

$2^n-1$

So, the given set has the elements -2, -1, 0, 1, 2, which means n = 5.

Then,

$\begin{gathered} 2^5=32 \\ 2^5-1=32-1=31 \end{gathered}$(a) The given set has 32 subsets.(b) The given set has 31 proper subsets.