Tuesday, April 15, 2014

Show that A ∩ B = A ∩ C need not imply B = C.

Show that A ∩ B = A ∩ C need not imply B = C. 
Answer
Let A = {0, 1}, B = {0, 2, 3}, and C = {0, 4, 5} Accordingly, A ∩ B = {0} and A ∩ C = {0}
Here, A ∩ B = A ∩ C = {0}
However, B ≠ C [2 ∈ B and 2 ∉ C]

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