Answer to Question #280415 in Discrete Mathematics for Ray

Question #280415

Find the sum-of-products expansions the Boolean function F(x, Y, 2) that equals 1 if and only if

a)x = 0.

b) xy = 0.

c) x +y = 0.

d)xyz = 0.



1
Expert's answer
2021-12-20T16:53:05-0500

a)

"\\overline{x}(yz+\\overline{y}z+y\\overline{z}+\\overline{y}\\overline{z})=\\overline{x}yz+\\overline{x}\\overline{y}z+\\overline{x}y\\overline{z}+\\overline{x}\\overline{y}\\overline{z}"


b)

"\\overline{xy }= \\overline {x}+\\overline{y}"

then:


"\\overline{xy}z+\\overline{xy}\\overline{z}=(\\overline {x}+\\overline{y})z+(\\overline{x}+\\overline{y})\\overline{z}=\\overline{x}z+\\overline{y}z+\\overline{x}\\overline{z}+\\overline{y}\\overline{z}"


c)

"\\overline{x +y}=\\overline{x}\\cdot \\overline{y}"

then:


"\\overline{x}\\cdot \\overline{y}\\cdot z+\\overline{x}\\cdot \\overline{y}\\cdot \\overline{z}"


d)

"\\overline{xyz}=\\overline{xy}+\\overline{z}=\\overline{x}+\\overline{y}+\\overline{z}"


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