Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Let a = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the Following Identitie: a − ( B ∩ C ) = ( a − B ) ∪ ( a − C ) - Mathematics

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie: 

\[A - \left( B \cap C \right) = \left( A - B \right) \cup \left( A - C \right)\] 

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Solution

Given:
A = {1, 2, 4, 5}, B = {2, 3, 5, 6} and C = {4, 5, 6, 7}
We have to verify the following identitie: 

\[A - \left( B \cap C \right) = \left( A - B \right) \cup \left( A - C \right)\] 

LHS 

\[(B \cap C) = {5, 6}\]
\[A - (B \cap C) = {1, 2, 4}\] 

RHS 

\[(A - B) = {1, 4}\]
\[(A - C) = {1, 2}\]
\[(A - B) \cup (A - C) = {1, 2, 4}\]

LHS = RHS
∴ \[A - \left( B \cap C \right) = \left( A - B \right) \cup \left( A - C \right)\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.6 | Q 2.5 | Page 27
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