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Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets1 Mark
Question
If A and B are two given sets, then $\text{A}\cap\text{(A}\cap\text{B})^\text{c}$ is equal to:
  1. $\text{A}$
  2. $\text{B}$
  3. $\phi$
  4. $\text{A}\cap\text{B}^\text{c}.$
✓

Answer

  1. $\text{A}\cap\text{B}^\text{c}.$

Solution:

A and B are two sets.

$\text{A}\cap\text{B}$ is the common region in both the sets.

$\text{A}\cap\text{B}^\text{c}$ is all the region in the universal set except $\text{A}\cap\text{B}.$

Now,

$\text{(A}\cap\text{A}\cap\text{B)}^\text{c}=\text{(A}\cap\text{B)}^\text{c}.$

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