Answer to Question #98516 in Discrete Mathematics for Ahmed

Question #98516
Use properties of Boolean algebra to simplify the following Boolean expression (show-
ing all the steps):
(x + y') (x + y')'
1
Expert's answer
2019-11-18T11:19:29-0500

Boolean expression


We need to simplify the given Boolean expression


Solution:


Some rules useful to simplify the Boolean expression



"1). \\space x + \\bar {x} = 1 \\\\ \n2).\\space x . \\bar {x} = \\space 0 \\\\ \n3). \\overline {x + y} = \\bar {x} . \\bar {y}"

Given,



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

"= ( x + \\bar {y} ) ( \\bar x . {x})= ( x + \\bar {y}) . 0 = 0"

Answer:

"(x + \\bar {y} ) (\\overline {x+ \\bar {y}} ) =" 0


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