IF A and b are two sets with n elements in common, then the number of elements common in a×b and b×a is
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Let A and B be two non-empty sets heaving n elements in common, then we have
(A×B)∩(C×D)=(A∩C)×(B∩D)
It is given that n(A∩B)=n elements
Now n[(A∩B)×(B∩A)]=n.n=n2 elements
Hence, A×B and B×A have n2 elements in common .
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