<s>[INST] boolean logic simplify To prove:
$(X+Y)(X'+Z) = XZ + X'Y$
I try to simply $(X+Y)(X'+Z)$ to $XZ + X'Y + YZ$
then I have no idea how to simply further.
Thanks in advance!!
 [/INST] $$\begin{align} (X + Y)(X' + Z) & = (X+Y)X' + (X+Y)Z \\ \\ & = \underbrace{X'X}_{= 0} + X'Y + XZ + YZ \\ \\ & = X'Y + XZ + YZ \\ \\ & = X'Y + XZ + \underbrace{(X+ X')}_{= 1}YZ \\ \\ & = X'Y + XZ + XYZ + X'YZ \\ \\ & = X'Y\underbrace{(1 + Z)}_{= 1} + XZ\underbrace{(1 + Y)}_{= 1} \\ \\ &= X'Y + XZ \end{align}$$
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