If $A=\{x \in R:|x|<2\}$ and $B=\{x \in R:|x-2| \geq 3\}$; then:

(A) $\mathrm{B}-\mathrm{A}=\mathrm{R}-(-2,5)$

(B) $\mathrm{A} \cap \mathrm{B}=(-2,-1)$

(C) $\mathrm{A}-\mathrm{B}=[-1,2)$

(D) $\mathrm{A} \cup \mathrm{B}=\mathrm{R}-(2,5)$

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Basic Mathematics

A = {x \in R : ∣ x ∣ < 2}

and

B = {x \in R : ∣ x - 2∣ \geq 3}

; then:

Answer: (A)

The sets are

A = {x : ∣ x ∣ < 2} = (- 2, 2)

and

B = {x : ∣ x - 2∣ \geq 3}

, which means

x - 2 \leq - 3

x - 2 \geq 3

, so

B = (- \infty, - 1] \cup [5, \infty)

. For

B - A

, remove from

B

anything lying in

(- 2, 2)

: intersecting

B

with the complement

(- \infty, - 2] \cup [2, \infty)

leaves

(- \infty, - 2] \cup [5, \infty)

, which is exactly

R - (- 2, 5)

. Hence

B - A = R - (- 2, 5)

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Single correct option