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

To find sets A, B and C such that A ∩ B = ϕ , A ∩ C = ϕ and A ∩ B ∩ C = ϕ

Take A = {1, 2, 3}

B = {2, 4, 6}

C = {3, 4, 7}

Then,

A ∩ B = {2}

∴ A ∩ B ≠ ϕ

A ∩ C = {3}

∴ A ∩ C ≠ ϕ

C ∩ B = {4}

∴ C ∩ B ≠ ϕ

But A, B and C do not have no elements in common,

∴ A ∩ B ∩ C = ϕ.