Question

Solve the problem in the picture.

Answer 1

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
`1`.

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}`