Boolean Alegebra De morgans rule 2

Question

hi i am told to perform a simplification using demorgans rule 2.

Here is the question

' = Equals Not

B . (C + B')'

I got

B' + (C' + B'') then

B' + (C' + B) Now i dont know where to go from here. Could you guys please help. Thank You

Answer 1

I think you've taken the negation of the expression you want. Consider:

B . (C + B')'

((B . (C + B')')')'

(B' + (C + B')'')'

(B' + (C + B'))'

...which doesn't look like a simplification at all. So, we simply negate the inner "or":

B . (C' . B'')

B . (C' . B)

Answer 2

$$B • \overline{ (C + \overline {B})}$$

Take DeMorgan's on second term. Remove complement, change operator (which you did not do) and complement terms.

$$B • (\overline {C} • \overline {\overline {B}})$$ $$B • \overline {C} • B$$

$ X•X = X $, which means:

$$B • \overline {C}$$