Question

Let $U=\{1,2,3,4,5,6\},A=\{2,3\}andB=\{3,4,5\}.Find{A}^{\prime },B^{\prime },A^{\prime }\cap B^{\prime },A\cup B$ and hence show that $(A\cup B)=A^{\prime }\cap B^{\prime }.$

Answer 1

A′=U−A={1,4,5,6}A′=U−A={1,4,5,6}
B′=U−B={1,2,6}B′=U−B={1,2,6}
A′∩B′={1,6}A′∩B′={1,6}
A∩B={2,3,4,5}A∩B={2,3,4,5}
∴(A∪B)′={1,6}=A′∩B′