Let A = {a, b, c}, B = {b, c, d, e} and = {c, d, e, f} be subsets of U = {a, b, c, d, e, f}. Then verify that:
(i) (A’)’ = A

(ii) (A ∪ B)’ = (A’ ∩ B’)

(iii) (A ∩ B)’ = (A’ ∪ B’)

Question

Philoid · Accepted Answer

(i) A’ = {d, e, f}

(A’)’ = {a, b, c} = A

Hence proved

(ii) AB = {a, b, c, d, e}

(AB)’ = {f}

A’ = {d, e, f}

B’ = {a, f}

A’B’ = {f}

(AB)’ = (A’B’)

Hence proved

(iii) A’B’ = {a, d, e, f}

AB = (b, c}

(AB)’ = {a, d, e, f}

(AB)’ = A’B’

Hence proved

Let A = {a, b, c}, B = {b, c, d, e} and = {c, d, e, f} be subsets of U = {a, b, c, d, e, f}. Then verify that:(i) (A’)’ = A(ii) (A ∪ B)’ = (A’ ∩ B’)(iii) (A ∩ B)’ = (A’ ∪ B’)