Let A and B be two sets containing 4 and 2 el | vedclass

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(B) Let $n(A) = 4$ and $n(B) = 2$. Then the number of elements in $A 	imes B$ is $n(A 	imes B) = 4 	imes 2 = 8$. The total number of subsets of $A

Vedclass · Accepted Answer

$219$

Vedclass · Answer

(B) Let $n(A) = 4$ and $n(B) = 2$. Then the number of elements in $A 	imes B$ is $n(A 	imes B) = 4 	imes 2 = 8$. The total number of subsets of $A 	imes B$ is $2^8 = 256$. We need to find the number of subsets having at least $3$ elements. This is equal to the total number of subsets minus the number of subsets having $0, 1,$ or $2$ elements. Number of subsets with $0$ elements = $\binom{8}{0} = 1$. Number of subsets with $1$ element = $\binom{8}{1} = 8$. Number of subsets with $2$ elements = $\binom{8}{2} = \frac{8 	imes 7}{2} = 28$. Total number of subsets with less than $3$ elements = $1 + 8 + 28 = 37$. Therefore,the number of subsets with at least $3$ elements = $256 - 37 = 219$.

Let $A$ and $B$ be two sets containing $4$ and $2$ elements respectively. Then the number of subsets of the set $A \times B$ each having at least $3$ elements is:

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