Question

3. If P = {a, b, c, d), Q = {d, e, f}. Prove the commutative property of union of sets.

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Answer 1

Answer:

We know that two sets A and B are commutative if A∪B=B∪A and A∩B=B∩A.

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

(i) A∪B=B∪A

A∪B={l,m,n,o,p,q}∪{m,n,o,r,s,t}={l,m,n,o,p,q,r,s,t}......(1)

B∪A={m,n,o,r,s,t}∪{l,m,n,o,p,q}={l,m,n,o,p,q,r,s,t}......(2)

From equations 1 and 2, we get that A∪B=B∪A.

(ii) A∩B=B∩A

A∩B={l,m,n,o,p,q}∪{m,n,o,r,s,t}={m,n,o}......(3)

B∩A={m,n,o,r,s,t}∪{l,m,n,o,p,q}={m,n,o}......(4)

From equations 3 and 4, we get that A∩B=B∩A.

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

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