How do I simplify the boolean expression A+A'BC+BC'?

Question

I'm trying to solve this:

So far I have:

a) a+b+c
b) a+bc
c) a+b
d) a+b

But for e) I can't progress further since I don't know how to deal with a'bc in this case. Can anyone help?

Answer 1

e) The expression is [a + (~a)bc + (~b)c]

a + [(~a)b + (~b)]c we can say that [(~a)b + (~b)] <--> [(~a) + (~b)] (Prove it by yourself:-)

a + [(~a) + (~b)]c

a + (~a)c + (~b)c we can say that [a + (~a)c] <--> [a + c]

a + c + (~b)c it is obvious that [c + (~b)c] <--> [c]

So [a + c] is the reduced expression.