Let $A, B, C$ be sets that are all contains in a universal group $U$. 3 out of 4 of 4 of these groups are equivalent. Which one isn't necessarily equivalent?

A. $((A \cap B) \cup (B \cap C)) \cap (\bar{A} \cup \bar{C})$

B. $(A \cap B) \triangle (C \cap B)$

C. $((A \cap B) \setminus C) \cup ((B \cap C) \setminus A)$

D. $(A \cap B) \setminus ( A \cap C)$

Where $\bar{A}$ is A's complement and $ \triangle$ is symmetric difference

I tried solving the question with venn diagrams but I couldn't really get this solved.

Can anyone please recommend an approach of solving this? I believe to have a good understanding of set operations but still having trouble solving this.



Suppose A= {a, b, c}, B= {a, c, d}, and C= {a, b, d} with U= {a, b, c, d, e}

Then $A\cap B=\{a\}$ and $B\cap C= \{a, d\}$ so $(A\cap B)\cup (B\cap C)= \{a, d\}$. $\overline{A}= \{d, e\}$ and $\overline{C}= \{c, e\}$ so that $\overline{A}\cup \overline{C}= \{c, d, e\}$. The intersection with the previous set is $\{d\}$. Do the same with each of the others.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.