Question

If A and B are two sets having 3 elements in common . If n(A) = 5, n(B)= 4 , then the number of elements in (A x B) ∩ (Bx A) is

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If A and B are two sets having 3 elements in common.If n(A)=5,n(B)=4, find n(A×B) and n[(A×B)∩(B×A)].

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ANSWER

Let A={a,b,c,d,e}

and B={1,2,3,4}

A×B=(a,1),(a,2),(a,3),(a,4),(b,1),(b,2),(b,3),(b,4),(c,1),(c,2),(c,3),(c,4),(d,1),(d,2),(d,3),(d,4),(e,1),(e,2),(e,3),(e,4)

∴n(A×B)=n(A)n(B)=20

We know that (A×B)∩(B×A)=(A∩B)×(B∩A)

So,(A×B)∩(B×A)=(A∩B)×(B∩A)

Given:Common elements of A and B=3

∴n(A∩B)=3

So,n[(A∩B)×(B∩A)]=n(A∩B)n(B∩A)=3×3=9 elements

∴n[(A∩B)×(B∩A)]=9 elements

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