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Let a = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the Following Identities: 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 identities: 

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

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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 identities: 

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

LHS

LaTeX

\[(B \cap C) = {5, 6}\]
\[A \cup (B \cap C) = {1, 2, 4, 5, 6}\] 
RHS 
\[\left( A \cup B \right) = {1, 2, 3, 4, 5, 6}\]
\[\left( A \cup C \right) = {1, 2, 4, 5, 6, 7}\]
\[\left( A \cup B \right) \cap \left( A \cup C \right) = {1, 2, 4, 5, 6}\] 
LHS = RHS
∴ \[A \cup \left( B \cap C \right) = \left( A \cup B \right) \cap \left( A \cup C \right)\]
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 2.1 | Page 27

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