Distributivity and P-o-S

The distrubitivity property will result in a Product-of-Sums expression

(as long as the expression does not have NAND or NOR)

f =(ab+c)(d+e) {apply yz+x=(y+x)(z+x)

= (a+c)(b+c)(d+e) with y=a, b=z, x=c}

g = abc+de {let x=abc, y=d, z=e, and

apply x+yz=(x+y)(x+z)}

=(abc+d)(abc+e)

=(ab+d)(c+d)(ab+e)(c+e)

=(a+d)(b+d)(c+d)(a+e)(b+e)(c+e)

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