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

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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).

  Is there an error in this question or solution?

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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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