Let $X$ be a non-empty set and let $A, B, C$ be subsets of $X$. Consider the following statments : (1) $\mathrm{A} \subset \mathrm{C} \Rightarrow(\mathrm{A} \cap \mathrm{B}) \subset(\mathrm{C} \cap \mathrm{B})(\mathrm{A} \cup \mathrm{B}) \subset(\mathrm{C} \cup \mathrm{B})$ (2) $(A \cap B) \subset(C \cap B)$ for all sets $B \Rightarrow A \subset C$ (3) $(\mathrm{A} \cup \mathrm{B}) \subset(\mathrm{C} \cup \mathrm{B})$ for all sets $\mathrm{B} \Rightarrow \mathrm{A} \subset \mathrm{C}$ Which of the above statements are correct?

• A

  1 and 2 only
• B

  2 and 3 only
• C

  1 and 3 only
• Correct answer
  D

  1,2 and 3

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