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

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

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Let A = {a, b}, B = {b, c} and C = {a, c}.

∴ A ∩ B = {b}, B ∩ C = {c}, A ∩ C = {a}

⇒A ∩ B, B ∩ C and A∩C are non-empty sets 

Now A ∩ B ∩ C = A ∩(5 ∩ C)

= {a, b} ∩ {c} = φ

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