self doubts

Question

how to simplify this boolean function i tend to get confuse on this given problem F(a,b,c)=(AB+AC)'+A'B'C

Answer 1

Simply expanding it : 

(AB+AC)' = (AB)'(AC)' [Demorgan] 

= (A'+B')(A'+C')

= A' + A'C' + A'B' + B'C'

A'(1+B'+C') + B'C'

= A' + B'C' [Absorption]

Or you can go by the good old K-map
 

	B'C'	B'C	BC	BC'
A'	1	1	1	1
A	1	0	0	0

Filled for (AB+AC)' : 

 

	B'C'	B'C	BC	BC'
A'	1	1	1	1
A	1	0	0	0

Add for A'B'C : It is already included from previous min-term.

From the above K Map

 F = A' + B'C'