1.

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

Answer»

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.



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