Answer to Question #98477 in Discrete Mathematics for Ahmed

Question

Use properties of Boolean algebra to simplify the following Boolean expression (show-
ing all the steps):
(x + y
0
)(x
0 + y
0
)
0

Answer 1

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

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 :

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