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Question
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that \[\left( A \cap B \right)' = A' \cup B'\]
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Solution
Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}
We have to verify:
\[\left( A \cap B \right)' = A' \cup B'\]
LHS
\[A \cap B = {2}\]
\[\left( A \cap B \right)' = {1, 3, 4, 5, 6, 7, 8, 9}\]
RHS
\[A' = {1, 3, 5, 7, 9}\]
\[B' = {1, 4, 6, 8, 9}\]
\[A' \cup B' = {1, 3, 4, 5, 6, 7, 8, 9}\]
LHS = RHS
Hence proved.
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