#### 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?

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