Let A and B be two sets containing four and two elements respectively.

Question

Let A and B be two sets containing four and
two elements respectively. Then, the number
of subsets of the set A $	imes$ B , each having atleast
three elements are

Accepted Answer

Given,

$\begin{gathered} n(A)=4,n(B)=2 \ \Rightarrow n(A	imes B)=8 \end{gathered}$

Total number of subsets of set $(A	imes B)={2}^{8}$

Number of subsets of set $A	imes B$ having no element (i.e. $\phi )=1$

Number of subsets of set $A	imes B$ having one element $={}^{8}{C}_{1}$

Number of subsets of set $A	imes B$ having two elements $={}^{8}{C}_{2}$

$	herefore $ Number of subsets having atleast three elements

$\begin{gathered} ={2}^{8}-(1+{}^{8}{C}_{1}+{}^{8}{C}_{2}) \ ={2}^{8}-1-8-28 \ ={2}^{8}-37 \ =256-37=219 \end{gathered}$

Solutions · 1