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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

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

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

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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: 

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

LHS 

\[(B \cup C) = {2, 3, 4, 5, 6, 7}\]
\[A \cap (B \cup C) = {2, 4, 5}\]

RHS

\[A \cap B = {2, 5}\]
\[A \cap C = {4, 5}\]
\[\left( A \cap B \right) \cup \left( A \cap C \right) = {2, 4, 5}\]

LHS = RHS 

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

Concept: Operations on Sets - Union Set
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.6 | Q 2.2 | Page 27

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