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:

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

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