Aspire Faculty ID #10695 · Topic: NIMCET 2021 · Just now
NIMCET 2021

If A={1,2,3,4} and B={3,4,5}, then the number of elements in (A∪B)×(A∩B)×(AΔB)

Solution

Given: \(A=\{1,2,3,4\}\), \(B=\{3,4,5\}\)

\(A\cup B=\{1,2,3,4,5\}\Rightarrow |A\cup B|=5\)
\(A\cap B=\{3,4\}\Rightarrow |A\cap B|=2\)
\(A\triangle B=(A\cup B)\setminus(A\cap B)=\{1,2,5\}\Rightarrow |A\triangle B|=3\)

Size of Cartesian product: \(|(A\cup B)\times(A\cap B)\times(A\triangle B)| = 5\times 2\times 3 = \mathbf{30}\).

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