Question

Let A and B be two non- empty sets. Prove that—
(i) if A=B then A×B=B×A
(ii) if A×B=B×A then A=B​

Answer 1

Answer:

In first part we will prove that if A=B then AxB=BxA and in the second part we will prove that if AxB=BxA then A=B. Then in AxB we can first replace first 'A' with 'B' (As by assumption A=B) so that it becomes BxB. Now we have AxB=BxB.