$4.(20$ points$)$ The following truth table represents a logic function $\backslash (\backslash$mathrm$\{$F$\}(\backslash$mathrm$\{$A$\},\backslash$mathrm$\{$B$\},\backslash$mathrm$\{$C$\})\backslash ).$ Use the truth table to write the expression for F in both Sum of Products $($SOP$)$ form and Product of Sums $($POS$)$ form.

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|\}$

$\backslash$hline$\backslash ($ A $\backslash )$ & $\backslash ($ B $\backslash )$ & $\backslash ($ C $\backslash )$ & $\backslash ($ F $\backslash )\backslash \backslash$

$\backslash$hline $0$ & $0$ & $0$ & $1\backslash \backslash$

$\backslash$hline $0$ & $0$ & $1$ & $0\backslash \backslash$

$\backslash$hline $0$ & $1$ & $0$ & $1\backslash \backslash$

$\backslash$hline $0$ & $1$ & $1$ & $0\backslash \backslash$

$\backslash$hline $1$ & $0$ & $0$ & $0\backslash \backslash$

$\backslash$hline $1$ & $0$ & $1$ & $1\backslash \backslash$

$\backslash$hline $1$ & $1$ & $0$ & $1\backslash \backslash$

$\backslash$hline $1$ & $1$ & $1$ & $0\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$