# Is this set statement true?

$$B \cap C \subseteq A \implies (C-A) \cap (B-A) = \varnothing.$$

I don't think this is true because B and neither C are necessarily a subset of A. Only B intercept C is a subset of A.

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how come b intercept c is a subset of a implies that b and c are a subset of a? i can draw a diagram where only b intercept c is a subset of a and a = b intercept c. – hjggh Oct 30 '12 at 19:18
The comment I made was when you had $B\cup C$ at the beginning, not $B\cap C$. Since it is not relevant to the changed question, I am deleting it. – André Nicolas Oct 30 '12 at 19:25

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