Question

For non empty subsets $A,B$ and $C$ of a set $X$, such that $A\cup B=B\cap C$. Which one of the following is the strongest inference that can be derived?

• A. $A=B=C$
• B. $A\subseteq B=C$
• C. $A=B\subseteq C$
• D. $A\subseteq B\subseteq C$

Answer 1

The correct option is D $A\subseteq B\subseteq C$

$A,B$ and $C$ are subset of set $X$.

$A\cup B=B\cap C$

$A$ and $B$ are subset of $C$.

Because $A\cup B=B\cap C$

So, $A\subseteq B\subseteq C$