Given A = {a,x,y,r,s},B = {1,3,5,7, -10}, verify the commutative property of set union.

The commutative property of set union says that for two given sets the value of their union 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

Here it’s given that

A = {a, x, y, r, s},

B = {1, 3, 5, 7, -10}

So using the data given

A ⋃ B = {a, x, y, r, s} ⋃ {1, 3, 5, 7, -10}

= {a, x, y, r, s, 1, 3, 5, 7, -10}…………………….(1)

B ⋃ A = {1, 3, 5, 7, -10} ⋃ {a, x, y, r, s}

= {1, 3, 5, 7, -10, a, x, y, r, s}

= {a, x, y, r, s, 1, 3, 5, 7, -10}……………………(2)

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