Solve the problem in the picture.

Question

asked Oct 3, 2022 221k views

1 Answer

Water · Answer 1 · 2022-10-08T01:00:07+0000

Answer:

See below

Explanation:

$\overline{X} \cdot\overline{Z} +\overline{X} \cdot Y + \overline{X} \cdot Z +XY$

$=\overline{X} (\overline{Z}+Y+Z) +XY$

Recall that

$\overline{Z} + Z = 1$

and the identity
$\boxed{A \cdot 1 = A}$ , therefore

$\overline{X} (\overline{Z}+Y+Z) = \overline{X}$ because
$\overline{Z}+Y+Z$ will always be
.

Thus,

$\overline{X} \cdot\overline{Z} +\overline{X} \cdot Y + \overline{X} \cdot Z +XY$

$=\overline{X} (\overline{Z}+Y+Z) +XY$

$= \overline{X} + XY$

Now considering the Absorption Law,

$( \overline{A} \cdot \overline{B}) + B = (\overline{A}+ B) \cdot (\overline{B} +B)$

Once
$\overline{B}+B=1$ , therefore

$\overline{A} +B$

we know

$= \overline{X} + XY = \boxed{\overline{X} +Y}$