Question

If $A$ and $B$ are two sets containing four and two elements, respectively. Then the number of subsets of the set $A\times B$ each having at least three elements is

• A. $219$
• B. $256$
• C. $275$
• D. $510$

Answer 1

Answer: (A)

$219$

$A=\{a,b,c,d\}$

$B=\{x,y\}$

$A\times B=2\times 4=8$ Elements.

Total number of subsets of $A\times B$ having $3$ or more elements $=2^8=256$

$\Rightarrow 256-(1$ null set $+$ $8$ singleton set $+$ ${}^8{e}_2$having $2$ elements$)$

$=256-1-8-28$

$=219$