Answer to Question #98516 in Discrete Mathematics for Ahmed

Question

Use properties of Boolean algebra to simplify the following Boolean expression (show-
ing all the steps):
(x + y') (x + y')'

Answer 1

Boolean expression

We need to simplify the given Boolean expression

Solution:

Some rules useful to simplify the Boolean expression

$$1). \space x + \bar {x} = 1 \\ 2).\space x . \bar {x} = \space 0 \\ 3). \overline {x + y} = \bar {x} . \bar {y}$$

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