Question

Verify the commutative property of union and intersection of sets for the following.
A = {l, m, n, o, p, q} B = {m, n, o, r, s, t}

Answer 1

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

The given sets are $A=${$l,m,n,o,p,q$} and $B=${$m,n,o,r,s,t$}

(i) $A\cup B=B\cup A$

$A\cup B=\{l,m,n,o,p,q\}\cup \{m,n,o,r,s,t\}=\{l,m,n,o,p,q,r,s,t\}......\left(1\right)B\cup A=\{m,n,o,r,s,t\}\cup \{l,m,n,o,p,q\}=\{l,m,n,o,p,q,r,s,t\}......\left(2\right)$

From equations 1 and 2, we get that $A\cup B=B\cup A$.

(ii) $A\cap B=B\cap A$

$A\cap B=\{l,m,n,o,p,q\}\cup \{m,n,o,r,s,t\}=\{m,n,o\}......\left(3\right)B\cap A=\{m,n,o,r,s,t\}\cup \{l,m,n,o,p,q\}=\{m,n,o\}......\left(4\right)$

From equations 3 and 4, we get that $A\cap B=B\cap A$.

Hence, the sets $A=${$l,m,n,o,p,q$} and $B=${$m,n,o,r,s,t$} are commutative.