What have you used ti simplify it in the first place? cause this isn't correct:
Simplest i have gotten is: A and B and C or (!A and !B) or (!A and !C) or (!B and !C)
Then it's not A and not B, it can also be not C, hence flase.
Theres similar errors with your last 2 as well.
Anyway, i got:
A!B!C + !AB!C + ABC + !A!BC
They're the 4 basic truth statements using AND, NOT and OR gates.
Although as CSflim said, they can be even simpler when using XOR gates.
A XOR B = A!B + !AB (ie when the 2 are different, the logic is true)
also A XNOR B is the inverse of this, so when they're the same the result is true.
eg A XNOR B = !A!B + AB
using this logic, you can simplify the first statment A!B!C + !AB!C + ABC + !A!BC to:
A(B XNOR C) + !A(B XOR C)
I
think this can then be simplified to:
A XOR (B XOR C)
So that'd be the simplest expression....
hope that helps
good luck
