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 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]
● 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
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