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Cartesian product of sets - class-XI
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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
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A
$219$
💡 Explanation:
$A=\left{a,b,c,d\right}$
$B=\left{x,y\right}$
$A\times B=2\times 4=8$ 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 $+$ $^8e _2$having $2$ elements$)$
$=256-1-8-28$
$=219$