Let A = \ 1, 2, 3, 4, 5, 6, 7\ and B =\ 3, 6, 7, 9\ . Then the...

Given,

$A = \left\{1, 2, 3, 4, 5, 6, 7\right\}$ and $B = \left\{3, 6, 7, 9\right\}$

We know that if any set has $n$ elements then total number of subset is given by ${2}^{n}$

So, total subset of $A = {2}^{7} = 128$

$C \cap B = ϕ$ when set $C$ contains the element $1, 2, 4, 5$

$∴ S = \left\{C ⊆ A; C \cap B \ne ϕ\right\}$

= Total$- \left(C \cap B = ϕ\right)$

$= 128 - {2}^{4} = 128 - 16 = 112$