Problems on Operation on Sets

1. Let A = {x : x is a natural number and a factor of 18}

B = {x : x is a natural number and less than 6}

Find A ∪ B and A ∩ B.

Solution:

A = {1, 2, 3, 6, 9, 18}

B = {1, 2, 3, 4, 5}

Therefore, A ∩ B = {1, 2, 3}


2. If P = {multiples of 3 between 1 and 20} and Q = {even natural numbers upto 15}. Find the intersection of the two given set P and set Q.
Solution:
P = {multiples of 3 between 1 and 20}
So, P = {3, 6, 9, 12, 15, 18}
Q = {even natural numbers upto 15}
So, Q = {2, 4, 6, 8, 10, 12, 14}
Therefore, intersection of P and Q is the largest set containing only those elements which are common to both the given sets P and Q
Hence, P ∩ Q = {6, 12}.