Let A= x ∈ R:|x+1|

Question

Let A= x ∈ R:|x+1|<2 and B = x ∈ R :| x -1| ≥ 2 . Then which one of the following statements is N O T true ? (A) A - B =(-1,1) (B) B - A = R -(-3,1) (C) A ∩ B =(-3,-1] (D) A ∪ B = R -[1,3)

Tardigrade Admin · Accepted Answer

A: x ∈(-3,1) B: x ∈(-∞,-1] ∪[3, ∞) B - A =(-∞,-3] ∪[3, ∞)= R -(-3,3)

Q. Let $A = {x \in R : ∣ x + 1∣ < 2}$ and $B = {x \in R : ∣ x - 1∣ \geq 2}$ . Then which one of the following statements is $NOT$ true ?

$A - B = (- 1, 1)$

$B - A = R - (- 3, 1)$

$A \cap B = (- 3, - 1]$

$A \cup B = R - [1, 3)$

$A : x \in (- 3, 1) B : x \in (- \infty, - 1] \cup [3, \infty)$
$B - A = (- \infty, - 3] \cup [3, \infty) = R - (- 3, 3)$

Q. Let A={x∈R:∣x+1∣<2} and B={x∈R:∣x−1∣≥2}. Then which one of the following statements is NOT true ?

A−B=(−1,1)

B−A=R−(−3,1)

A∩B=(−3,−1]

A∪B=R−[1,3)