Question

Verify the commutative property of set intersection for $A=\{l,m,n,o,2,3,4,7\}$ and $B=\{2,5,3,-2,m,n,o,p\}$.

Answer 1

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

Here, the given sets are $A=\{l,m,n,o,2,3,4,7\}$ and $B=\{2,5,3,-2,m,n,o,p\}$

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

$A\cap B=\{l,m,n,o,2,3,4,7\}\cap \{2,5,3,-2,m,n,o,p\}=\{m,n,o\}........\left(1\right)$

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

$B\cap A=\{2,5,3,-2,m,n,o,p\}\cap \{l,m,n,o,2,3,4,7\}=\{m,n,o\}........\left(2\right)$

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

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