Question

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

Answer 1

We know that two sets $A$ and $B$ are said to be commutative if $A\cup B=B\cup A$.

Here, the given sets are $A=\{a,x,y,r,s\}$ and $B=\{1,3,5,7,-10\}$

Let us first find $A\cup B$ as follows:

$A\cup B=\{a,x,y,r,s\}\cup \{1,3,5,7,-10\}=\{a,x,y,r,s,1,3,5,7,-10\}........\left(1\right)$

Now we find $B\cup A$as follows:

$B\cup A=\{1,3,5,7,-10\}\cup \{a,x,y,r,s\}=\{a,x,y,r,s,1,3,5,7,-10\}........\left(2\right)$

Since equation 1 is equal to equation 2, therefore $A\cup B=B\cup A$.

Hence, the the sets $A$ and $B$ satisfies the commutative property of union.