Question

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

Answer 1

It is given that,

A∩B≠ϕ(1)

B∩C≠ϕ(2)

A∩C≠ϕ(3)

A∩B∩C=ϕ(4)

From condition (1), some of the elements are common in A and B. From condition (2), some of the elements are common in B and C. From condition (4), there should not be any common element between A B and C.

From the given condition, let’s assume,

A={ 1,2 } B={ 2,3 } C={ 3,4 }

These sets satisfy all the four conditions.

Thus, A∩B∩C=ϕ.