For sets $S$ and $T$, define
$S \backslash T=\{x \in S: x \notin T\} .$
Let $P, Q$ and $R$ be distinct sets. Then

• A

  $P \cup(Q \backslash P)=Q$
• Correct answer
  B

  if $R \subset Q$ then $P \cap(R \cup(Q \backslash R))=P \cap Q$
• C

  $P \cup(Q \backslash R)=(P \cup Q) \backslash(P \cup R)$
• D

  if $R \subset P$ then $P \cap(R \cup(Q \backslash R))=P \cap Q$.

Hence, the correct answer is option: 'B'.