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Sets — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSets1 Mark
MCQ
If $A$ and $B$ are non empty sets and $A'$ and $B'$ represents their compliments respectively then:
  • A
    $\ce{A − B = A′ − B′}$
  • B
    $\ce{A − A ′ = B − B′}$
  • ✓
    $\ce{A − B = B′ − A′}$
  • D
    $\ce{A − B′ = A′ − B}$
✓

Answer

Correct option: C.
$\ce{A − B = B′ − A′}$
Let $U \rightarrow$ Universal set
$X \rightarrow \ce{U - (A + B)}$
$\ce{B′ = X + A}$
$\ce{A′ = X + B}$
$\ce{B′ - A′ = X + A - (X + B)}$
$= \ce{X + A - X - B}$
$\ce{B′ - A′ = A - B}$

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