1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A= x: x ∈ R, x<1 ; B= x: x ∈ R, x-1 ≥ and A ∪ B=R-D, then the set D is

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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

BITSATBITSAT 2010

Solution:

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