Question

Example 1.29. If U = (1, 2, 3, 4, ..., 10), A = (2, 4, 6, 8), B = (1, 3, 5, 7, 9), and C = (2, 3, 5, 7), verify
that
(i) (A UC)' = A'C'
(ii) (BU C'= B'C'
(ii) (A UB)' = A' B'
(iv) U' = 0 and O' = U
Also, find [(A UB UC).​

Answer 1

Answer:

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B)

′

=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}

=ϕ

A

′

∩B

′

=(U−A)n(U−B)

={3,4,6}n{1,2,7}

=ϕ

Hence (A∪B)

′

=A

′

∩B

′

.