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Let $U = \{a,b,c,...,x,y,z\}$ with $A=\{a,b,c \}$ and $C=\{a,b,d,e \}$. If $|A \cap B| = 2$ and $(A \cap B) \subset B \subset C$, determine $B$.

This question doesn't seem complete. Am I right, and if not, what is the answer?

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    What does $X \subset Y$ mean: "$X$ is a subset of $Y$" or "$X$ is a *proper* subset of $Y$"?2011-09-16
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    >If C, D are sets from a universe U, C is a subset of D, written C ⊆ D, or D ⊇ C, if every element of C is an element of D. Additionally, if D contains an element that is not in C, then C is called a proper subset of D, denoted C ⊂ D or D ⊃ C.2011-09-16
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    The question seems ambiguous. B can be either {a, b, d} or {a, b, e}.2011-09-16
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    a930913 Yes, the terms *subset* and *proper subset* are standard and I understand them. On the other hand, the notation $\subset$ is used to mean both "subset" and "proper subset" (depending on who uses it). That's why I commented asking you to clarify what you mean by it. (Some people, like me, use the more emphatic notations $\subseteq$ and $\subsetneq$, avoiding $\subset$ altogether.)2011-09-16

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