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?
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?
if we are taking the subsets to be proper, then the possible answers are B={a,b,d} and B={a,b,e}, if the symbol admits subsets that are not proper, then we can also have B=C and B={a,b}. In both cases there is not a unique answer.
Hint: $ c \not \in B$, so what is $A \cap B$? But I don't see how you can tell the difference between $d$ and $e$. If $\subset$ is proper subset you can get pretty close.
If inclusion is proper then $B=\{a,b,d\}$ or $B=\{a,b,e\}$ and if inclusion covers equality, than one could add $\{a,b\}$ and $\{a,b,d,e\}$.