Question

A and B are two sets having 3 elements in common. If n(A)=5 and n(B)=6, find n((A×B)n(B×A))
chapter-sets
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Answer 1

Step-by-step explanation:

We know that (A×B)∩(B×A)=(A∩B)×(B∩A)

So,n[(A×B)∩(B×A)]=n[(A∩B)×(B∩A)]

Given:Common elements of A and B=3

∴n(A∩B)=n(B∩A)=3

So,

n[(A∩B)×(B∩A)]=n(A∩B)n(B∩A)=3×3=9

∴n[(A∩B)×(B∩A)]=9 elements