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For Any Two Sets a and B, Prove the Following: a ∩ ( a ∪ B ) ′ = ϕ - Mathematics

For any two sets A and B, prove the following: 

\[A \cap \left( A \cup B \right)' = \phi\] 

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Solution

\[LHS = A \cap \left( A \cup B \right)'\]
\[ = A \cap \left( A' \cap B' \right)\]
\[ = \left( A \cap A' \right) \cap \left( A \cap B' \right)\]
\[ = \left( \phi \right) \cap \left( A \cap B' \right) \]
\[ = \phi = RHS \left[ \phi \cap A = \phi \right]\] 

Hence proved.

Concept: Universal Set
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.7 | Q 2.3 | Page 34
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