Simplifying Boolean algebra expression with two brackets

Question

Could someone please show me how to get the answer? The correct answer is c):

Simplify the following Boolean algebraic expressions (where ’ means not):
A.B’ + A.(B + C)’ + B.(B + C)’

a) B.C’
b) B + C
c) A.B’
d) A + B’
e) None of the above

@Gamopo sorry i forgot to mentinon that, it equivalent to NOT. — Reix, Jan 16 '20 at 17:22
Are you sure that it is A.B’ + A.(B + C)’ + B.(B + C)’ instead of A.B’ + C.(B + C)’ + B.(B + C)’? I mean changing A for C in the second part? — Gamopo, Jan 16 '20 at 17:24
@Gamopo Yeah i copied and pasted it exactly from the sheet. im so confused xD — Reix, Jan 16 '20 at 17:26

score 1 · Answer 1 · edited Apr 24 '21 at 14:08

1

First simplify the parentheses

A.B’ + A.(B + C)’ + B.(B + C)’=
A.B’ + A.B’.C’ + B.B’.C’

Now B.B’=0 so the third term is gone:

A.B’ + A.B’.C’

Now you can regroup A.B’:

A.B’.(1 + C’)

Finally 1+C’=1 so all that's left is

A.B’

edited Apr 24 '21 at 14:08

Will Ness

answered Jan 16 '20 at 18:16

Gamopo

1 Answers1