Let A= x: x ∈ R, x

Question

Let A= x: x ∈ R, x<1 ; B= x: x ∈ R, x-1 ≥ and A ∪ B=R-D, then the set D is (A)  x :1 < x le 2  (B)  x :1 le x < 2  (C)  x :1 le x le 2  (D) None of these

Tardigrade Admin · Accepted Answer

A=[x: x ∈ R,-1 < x < 1] B=[x: x ∈ R: x-1 ≤-1 or x-1 ≥ 1] =[x: x ∈ R: x ≤ 0 or x ≤ 2] ∴ A ∪ B =R-D where D=[x: x ∈ R, 1 ≤ x<2]

Q. Let $A = {x : x \in R, x < 1}; B = {x : x \in R, x - 1 \geq}$ and $A \cup B = R - D$ , then the set $D$ is

${x : 1 < x \leq 2}$

${x : 1 \leq x < 2}$

${x : 1 \leq x \leq 2}$

None of these

$A = [x : x \in R, - 1 < x < 1]$
$B = [x : x \in R : x - 1 \leq - 1$ or $x - 1 \geq 1]$
$= [x : x \in R : x \leq 0$ or $x \leq 2]$
$∴ A \cup B = R - D$
where $D = [x : x \in R, 1 \leq x < 2]$

Q. Let A={x:x∈R,x<1};B={x:x∈R,x−1≥} and A∪B=R−D, then the set D is

{x:1<x≤2}

{x:1≤x<2}

{x:1≤x≤2}