Question
Let $$A,\,B,\,C$$ are three non-empty sets. If $$A \subset B$$ and $$B \subset C,$$ then which of the following is true ?
A.
$$B - A = C - B$$
B.
$$A \cap B \cap C = B$$
C.
$$A \cup B = B \cap C$$
D.
$$A \cup B \cup C = A$$
Answer :
$$A \cup B = B \cap C$$
Solution :
If $$A \subset B$$ and $$B \subset C,$$ then these sets is represented in Venn diagram as
$$\eqalign{ & {\text{Clearly }}A \cup B = B{\text{ and }}B \cap C = B \cr & {\text{Hence}}{\text{,}}\,\,A \cup B = B \cap C \cr} $$
If $$A \subset B$$ and $$B \subset C,$$ then these sets is represented in Venn diagram as
$$\eqalign{ & {\text{Clearly }}A \cup B = B{\text{ and }}B \cap C = B \cr & {\text{Hence}}{\text{,}}\,\,A \cup B = B \cap C \cr} $$