Answer:
See below
Step-by-step explanation:
[tex]\overline{X} \cdot\overline{Z} +\overline{X} \cdot Y + \overline{X} \cdot Z +XY[/tex]
[tex]=\overline{X} (\overline{Z}+Y+Z) +XY[/tex]
Recall that
[tex]\overline{Z} + Z = 1[/tex]
and the identity [tex]\boxed{A \cdot 1 = A}[/tex], therefore
[tex]\overline{X} (\overline{Z}+Y+Z) = \overline{X}[/tex] because [tex]\overline{Z}+Y+Z[/tex] will always be [tex]1[/tex].
Thus,
[tex]\overline{X} \cdot\overline{Z} +\overline{X} \cdot Y + \overline{X} \cdot Z +XY[/tex]
[tex]=\overline{X} (\overline{Z}+Y+Z) +XY[/tex]
[tex]= \overline{X} + XY[/tex]
Now considering the Absorption Law,
[tex]( \overline{A} \cdot \overline{B}) + B = (\overline{A}+ B) \cdot (\overline{B} +B)[/tex]
Once [tex]\overline{B}+B=1[/tex], therefore
[tex]\overline{A} +B[/tex]
we know
[tex]= \overline{X} + XY = \boxed{\overline{X} +Y}[/tex]
