Answer to Question #98477 in Discrete Mathematics for Ahmed

Question #98477
Use properties of Boolean algebra to simplify the following Boolean expression (show-
ing all the steps):
(x + y
0
)(x
0 + y
0
)
0
1
Expert's answer
2019-11-13T11:55:58-0500

"( x + \\overline y) \\overline{(\\overline x +\\overline y)}"

we know,

"\\overline {A+ B} = \\overline A . \\overline B \\space and \\space \\overline{\\overline A} = A"

"( x + \\overline y) \\overline{(\\overline x +\\overline y)} = ( x + \\overline y) ( \\overline{(\\overline x} * \\overline{\\overline y}))"

"= (x + \\overline y) ( x *y)"

"= x . x . y + x y .\\overline y = x . y + 0 = x. y"

Since

"( x . x = x \\space and \\space y .\\overline y = 0)"

Answer :

"( x + \\overline y) \\overline{(\\overline x +\\overline y)} = x. y"


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