Question

Test for the commutative property of union and intersection of the sets P = { x : x is a real number between 2 and 7} and Q = { x : x is an irrational number between 2 and 7}.

Answer 1

P = {x : x is a real number between 2 & 7}

Q = {x : x is an irrational no.between 2 & 7}

Clearly, P contains all rational and irrational numbers between 2 and 7.

Then,

PUQ and QUP, each of them contains all real numbers between 2 and 7.

Hence they are equal.

Moreover, Q is a proper subset of P

Then PnQ = QnP = Q

Hence commutative property is verified.

I hope this answer helps you