Question

Let $A$ and $B$ be two sets containing $2$ elements and $4$ elements respectively. The number of subsets of $A\times B$ having $3$ and more elements is

• A. $219$
• B. $211$
• C. $256$
• D. $220$

Answer 1

The correct option is A $219$

$A=\{x,y\}$

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

$A\times B=2\times 4=8$ elements

Total sunsets $=2^8=256$

total number of subsets of $A\times B$

=256-(1 null set + 8 single ton set + ${}^8{C}_2$ having 2 elements)

$=256-1-8=219$