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 or more elements is

• A. $200$
• B. $219$
• C. $211$
• D. $256$

Answer 1

The correct option is B $219$

Now according to the given condition, the number of subsets will be

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

$B=\{x,y\}$

Total number of elements in $A\times B=8$

Total number of subsets in $A\times B=2^8=256$

Number of subsets having $3$ or more elements = $256$ - ( no. of subsets having ($1$ element + $2$ elements + $0$ elements)

= $2^8{-}^8{C}_0{-}^8{C}_1{-}^8{C}_2=256-1-8-28=219.$