Combinational Logic - Need help with proof by rewrite
The last line is wrong : 
1    1    1    1
Should be : 
1    1    1    0

But the equations following are correct.

For the simplification :
BC’ + B’C + AB’C’ = BC' + B'.(C+AC') = BC'+B'.(C+A)=BC'+B'C+B'A

(I don't know the name of the rules used, there is some associativity, "X+X'Y = X+Y", etc...)

--- edit ---

Let's prove that X+X'Y = X+Y

Using :


A = A.B + A.B'
A = A+A
A + AB = A.(1+B) = A
A + A' = 1


X+X'Y = XY+XY'+X'Y = Y(X+X') + XY' = Y + XY'

Repeating (A=A+A) :

X+X'Y = X+X'Y + X+X'Y = X+X'Y + Y+XY' 

= X + Y + X'Y + XY' 

= X+XY' + Y+X'Y

= X + Y