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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 = ∅

Solution:

Let A={0,1}, B={1,2}, and C={2,0}. Accordingly, A∩B={1}, B∩C={2}, A∩C={0}.
∴A∩B, B∩C, and A∩C are non-empty. However, A∩B∩C=∅