Let $\mathrm{A}, \mathrm{B}$ and C be sets such that $\phi \neq \mathrm{A} \cap \mathrm{B} \subseteq \mathrm{C}$. Then which of the following statements is not true?

(A) If $(A-C) \subseteq B$, then $A \subseteq B$

(B) If $(A-B) \subseteq C$, then $A \subseteq C$

(C) $(C \cup A) \cap(C \cup B)=C$

(D) $\mathrm{B} \cap \mathrm{C} \neq \phi$

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Sets Relations and Functions

Let

A, B

and C be sets such that

ϕ \neq = A \cap B \subseteq C

. Then which of the following statements is not true?

Answer: (A)

With

\emptyset \neq = A \cap B \subseteq C

, test each claim. The statement that

(A - C) \subseteq B

forces

A \subseteq B

fails: take

A = {1, 2}

B = {1, 3}

C = {1, 2}

. Here

A \cap B = {1} \subseteq C

and

A - C = \emptyset \subseteq B

, yet

2 \in A

is not in

B

, so

A \neq \subseteq B

. The other three statements hold in general, so the one that is not true is this first claim.

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option