Prove that

Question:

Prove that $A \times B=B \times A \Rightarrow A=B$.

 

Solution:

Let A and B be any two sets such that

$A \times B=\{(a, b): a \in A, b \in B\}$

Now,

$B \times A=\{(b, a): a \in A, b \in B\}$

A × B = B × A

(a, b) = (b, a)

We can see that this is possible only when the ordered pairs are equal.

Therefore,

a = b and b = a

Hence, Proved

 

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