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Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets1 Mark
MCQ
For any two sets A and B, $\text{A}\cap\text{(A}\cup\text{B)}'$ is equal to:
  • A
    $\text{A}$
  • B
    $\text{B}$
  • ✓
    $\phi$
  • D
    $\text{A}\cap\text{B}.$
✓

Answer

Correct option: C.
$\phi$
$\text{A}\cap\text{(A}\cup\text{B)}'$
$=\text{A}\cap\text{(A}'\cup\text{B}')$ (De Morgen Law)
$=\text{(A}\cap\text{A}')\cap\text{B}'$
$=\phi\cap\text{B}'$
$=\phi$
Hence, the correct answer is option (c).

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