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