+1 vote
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Find the complement of X + YZ; then show that F.F’=0 and F + F’ = 1
| 59 views

Given expression$=X+YZ$

Complement of that expression $=\overline{X+YZ}=\overline{X}\cdot\overline{YZ}=\overline{X}\cdot(\overline{Y}+\overline{Z})$

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

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Show that ${\color{Red}{F\cdot\overline{F}=0} }$ and ${\color{Magenta} {F+\overline{F}=1}}$

Lets make truth table for clear understanding

 $F$ $\overline{F}$ $F\cdot \overline{F}$ 0 1 0 1 0 0

and

 $F$ $\overline{F}$ $F+\overline{F}$ 0 1 1 1 0 1

we can also do this using truth table

+1 vote