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.

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

Sets Theory

Representation of a Set

Types of Sets

Finite Sets and Infinite Sets

Power Set

Problems on Union of Sets

Problems on Intersection of Sets

Difference of two Sets

Complement of a Set

Problems on Complement of a Set

Problems on Operation on Sets

Word Problems 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

Examples on Venn Diagram



8th Grade Math Practice

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