Show that A intersection B is equal to A intersection C need not imply B=C

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Solution

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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Similar questions

A \cap B = A \cap C

B = C

For three sets A, B and C, show that

(i) $A \cap B = A \cap C$ need not imply B = C.

(ii) $A \subset B \Rightarrow C - B \subset C - A$

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