Find the sum of product expansion of the Boolean function f(x,y,z) = (x+z)y

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$F(x,y,z)=(x+z)y$

To determine the sum of product expansion of $F$ , we could use boolean identities or construct a table that determines all values of $F$ . I will be using boolean identities.

$F(x,y,z)=(x+z)y$

$=xy+zy \text{ (Distributive Law) }\\ =xy.1+zy.1 \text{ (Identity Law) }\\ =xy(z+ \bar{z})+zy(x+\bar{x}) \text{ (Unit Property) }\\ =xyz+xy\bar{z}+zyx+zy\bar{x} \text{(Distributive Law) }\\ =xyz+xy\bar{z}+xyz+\bar{x}yz \text{ (Commutative Law) }\\ =xyz+xy\bar{z}+\bar{x}yz \text{(Idempotent Law) }$

Find the sum of product expansion of the Boolean function f(x,y,z) = (x+z)y

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Question ID: mtid-5-stid-8-sqid-3430-qpid-2129