Verify the commutative property of set intersection for

A = {m, n, o, 2, 3, 4, 7} and B = {2, 5, 3, - 2, m, n, o, p}.

The commutative property of set intersection says that for two given sets the value of their intersection are commutative in nature.

Mathematically, if A and B are two sets with a number of elements then with the help of commutative property of set theory we can conclude that

A ⋂ B = B ⋂ A

It’s given that

A = {m, n, o, 2, 3, 4, 7}

B = {2, 5, 3, - 2, m, n, o, p}.

So using given data

A ⋂ B = {m, n, o, 2, 3, 4, 7} ⋂ {2, 5, 3, - 2, m, n, o, p}.

= {m, n, o, 2, 3}…………….. (1)

Similarly

B ⋂ A = {2, 5, 3, - 2, m, n, o, p} ⋂ {m, n, o, 2, 3, 4, 7}

= {2, 3, m, n, o}

= {m, n, o, 2, 3}……………….. (2)

So from (1) an (2) it’s clear that the set intersection operation is commutative in nature i.e. A ⋂ B = B ⋂ A (proved)