Answer to Question #234644 in Algebra for bee

Question

Find the complement of the function using De Morgan's method:

1. Q = ((AB + (BC)') + A)'

2. Q = ((AB'C)' + (B + C')')'

Answer 1

1.(AB + (BC)') + A)'=((AB + (B'+C') + A)'[Using De morgan's first theorem]

=(A'+B')(BC)A'[Using De morgan's second theorem]

2. Q = ((AB'C)' + (B + C')')'

=((A'+B+C)+(B'C))' [Using De morgan's first theorem]

=(AB'C')(B+C')[Using De morgan's second theorem] and Since (A')'=A