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  4. If A= 1,2,3,4 B= 3,4,5 then the number of elements in (A ∪ B) ×(A ∩ B) ×(A Δ B) is

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Q. If $A=\{1,2,3,4\}, B=\{3,4,5\}$ then the number of elements in $(A \cup B) \times(A \cap B) \times(A \Delta B)$ is

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Solution:

$ A \cup B=\{1,2,3,4,5\} . n(A \cup B)=5 $
$A \cap B=\{3,4\}, n(A \cap B)=2$
$A \Delta B=(A \sim B) \cup(B \sim A)=\{1,2\} \cup\{5\}$
$=\{1,2,5\} $
$n(A \Delta B)=3 . \text { Hence } n((A \cup B) \times(A \cap B) \times(A \Delta B)\} $
$=5 \times 2 \times 3=30 .$