A and B are two subsets of set S = {1, 2, 3, | vedclass

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(B) For each element $x \in S$,there are four possibilities for its membership in sets $A$ and $B$ such that $x \in A \cup B$:$1$. $x \in A$ and $x

Vedclass · Accepted Answer

$81$

Vedclass · Answer

(B) For each element $x \in S$,there are four possibilities for its membership in sets $A$ and $B$ such that $x \in A \cup B$:$1$. $x \in A$ and $x 
otin B$$2$. $x 
otin A$ and $x \in B$$3$. $x \in A$ and $x \in B$Since $A \cup B = S$,the case where $x 
otin A$ and $x 
otin B$ is excluded.Thus,for each of the $4$ elements in $S$,there are $3$ choices.Since there are $4$ elements in $S$,the total number of ordered pairs $(A, B)$ is $3 	imes 3 	imes 3 	imes 3 = 3^4 = 81$.

$A$ and $B$ are two subsets of set $S = \{1, 2, 3, 4\}$ such that $A \cup B = S$. Find the number of ordered pairs $(A, B)$.

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