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 |
