Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = φ

Solution:

The intersection of two given sets is the set that contains all the elements that are common to both sets.

The symbol for the intersection of sets is "∩''.

For any two sets A and B, the intersection, A ∩ B (read as A intersection B) lists all the elements that are present in both sets, the common elements of A and B.

Let A = {1, 2}, B = {2, 3} , and C = {1, 3}

We can see that

A ∩ B = {2}, B ∩ C = {3} and A ∩ C = {1}

Hence,

A ∩ B, B ∩ C and A ∩ C are non-empty.

However,

A ∩ B ∩ C = Φ

NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 12

Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = φ.

Summary:

Sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = φ are A = {1, 2}, B = {2, 3} , and C = {1, 3} respectively.