Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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For Any Two Sets a and B, Prove that a − ( a ∩ B ) = a − B - Mathematics

For any two sets A and B, prove that \[A - \left( A \cap B \right) = A - B\] 

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Solution

\[A - \left( A \cap B \right) = A \cap \left( A \cap B \right)' \left( X - Y = X \cap Y' \right)\]
\[ = A \cap \left( A' \cup B' \right) \left( \text{ De Morgan law } \right)\]
\[ = \left( A \cap A' \right) \cup \left( A \cap B' \right)\]
\[ = \phi \cup \left( A \cap B' \right)\]
\[ = A \cap B'\]
\[ = A - B\]

Concept: The Empty Set
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.7 | Q 4.2 | Page 35
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