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

Answer 1

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:

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

LHS 

\[A \cup B = {2, 3, 4, 5, 6, 7, 8}\]
\[\left( A \cup B \right)' = {1, 9}\]

RHS 

\[A' = {1, 3, 5, 7, 9}\]
\[B' = {1, 4, 6, 8, 9}\]
\[A' \cap B' = {1, 9}\] 

LHS = RHS
Hence proved.