Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 11
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# For Any Two Sets a and B, a ∩ ( a ∪ B ) ′ is Equal to - Mathematics

ConceptPractical Problems on Union and Intersection of Two Sets

#### Question

For any two sets A and B, $A \cap \left( A \cup B \right)'$is equal to

• (a) A

•  (b) B

•  (c)$\phi$

•  (d)$A \cap B$

#### Solution

$A \cap \left( A \cup B \right)'$

$= A \cap \left( A' \cap B' \right) \left( \text{ De Morgan law } \right)$

$= \left( A \cap A' \right) \cap B'$

$= \phi \cap B'$

$= \phi$

Hence, the correct answer is option (c).

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Solution For Any Two Sets a and B, a ∩ ( a ∪ B ) ′ is Equal to Concept: Practical Problems on Union and Intersection of Two Sets.
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