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