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.


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