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Sets — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSets1 Mark
MCQ
Let $A$ and $B$ be two sets such that $A ∩ B = ϕ.$ Find the value of $(A ∪ B′) =$
  • A
    $A′$
  • ✓
    $B$
  • C
    $ϕ$
  • D
    none of these.
✓

Answer

Correct option: B.
$B$
Given, $\ce{A ∩ B} = ϕ.$
Now,
$\ce{(A ∪ B′)}$
$= \ce{(A′ ∩ B)′} [$Using De Morgan's law$]$
$= \ce{B′}.[$ As $\ce{A′ ∩ B = B − (A ∩ B) = B}$ since $\ce{A ∩ B} = ϕ]$

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