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.
Click Here to know more about the operations on intersection of 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 workedout 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]
● Set Theory
● Finite Sets and Infinite Sets
● Problems on Intersection of Sets
● Problems on Complement of a Set
● Problems on Operation on Sets
● Venn Diagrams in Different Situations
● Relationship in Sets using Venn Diagram
● Union of Sets using Venn Diagram
● Intersection of Sets using Venn Diagram
● Disjoint of Sets using Venn Diagram
● Difference of Sets using Venn Diagram
8th Grade Math Practice
From Problems on Intersection of Sets to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.