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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.
Solution
Let A = {1, 2}, B = {2, 3}, C = {1, 3}
A ∩ B = {1, 2} ∩ {2, 3} = {2}
B ∩ C = {2, 3} ∩ {1, 3} = {3}
C ∩ A = {1, 3} ∩ {1, 2} = {1}
Hence, A ∩ B, B ∩ C, C ∩ A is not the empty set.
A ∩ B ∩ C = (A ∩ B) ∩ C
= {2} ∩ {1, 3} = ϕ.
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