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Question
Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie:
\[A \cap \left( B \cup C \right) = \left( A \cap B \right) \cup \left( A \cap C \right)\]
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:
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
∴ \[A \cap \left( B \cup C \right) = \left( A \cap B \right) \cup \left( A \cap C \right)\]
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