Problems on Intersection of Sets

Solved problems on intersection
of sets are given below to get a fair idea how to find the intersection of two or more sets.

We know, the intersection of two or more sets is a set which contains all the elements that are common in those sets.

Solved problems on intersection of 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}.

More worked-out problems on union of sets to find the intersection of
three sets.

3. Let A = {0, 1, 2, 3, 4, 5}, B = {2,
4, 6, 8} and C = {1, 3, 5, 7}

Verify (A ∩ B) ∩ C = A ∩ (B ∩ C)

Solution:

(A ∩ B) ∩ C = A ∩ (B ∩ C)

L.H.S. = (A ∩ B) ∩ C

A ∩ B = {2, 4}

(A ∩ B) ∩ C = {∅} ……………….. (1)

R.H.S. = A ∩ (B ∩ C)

B ∩ C = {∅}

A ∩ {B ∩ C} = {∅} ……………….. (2)

Therefore, from (1) and (2), we conclude that;

(A ∩ B) ∩ C = A ∩ (B ∩ C)  [verified]