You are given the following truth table for a $3-$input logic function F$($A$,$ B$,$ C$)$:

A B C F

$0001$

$0010$

$0100$

$0111$

$1001$

$1010$

$1100$

$1111$

Using Karnaugh Maps, simplify the expression for F$($A$,$ B$,$ C$)$ and write the simplified Boolean expression.