Answer to Question #170983 in Discrete Mathematics for altair

Question

Simplify ((A U B') n C) U(A'n B)' and write the dual of the result.

Answer 1

[(A U B') n C] U(A'n B)' 

[(A n C) u (B' n C)] u (A' n B)'

(A n C) u (B' n C) u (A' n B)'

(A n C) u (B u C')' u (A' n B)'

(A n C) u [(B u C') n (A' n B)]'

(A n C) u [(B n A' n B) u (C' n A' n B)]'

(A n C) u [(A' n B) u (A' n B n C')]'

(A n C) u (A' n B)'------*

[(A n C) u A] n [(A n C) u B']

=A n [(A n C) u B']-----**

Recall that

A'' = A

A n (B u C) = (A n B) u (A n C)

(A u B)' = A' n B'

If A $\subset$ B ; then A n B = A

If A $\subset$ B ; then A u B = B