Question

If P = Q then P X Q = Q X P is true or not?

(a) True

(b) False

This question was posed to me in an internship interview.

Enquiry is from Cartesian Product of Sets in division Relations and Functions of Mathematics – Class 11

Answer 1

The correct option is (a) True

The best explanation: Let P = (x, y) and Q = (a, b)

P X Q = {(x, a), (x, b), (y, a), (y, b)}

Q X P = {(a, x), (a, y), (b, x), (b, y)}

If P = Q i.e. x=a and y=b then P X Q = {(a, a), (a, b), (b, a), (b, b)}

Q X P = {(a, a), (a, b), (b, a), (b, b)}.

Hence P X Q = Q X P.