Part a $[10$ Points$]$ For the given Truth table, design and draw the logic circuits for F using Decoder and Multiplexer with additional minimum logic elements. A$,$ B$,$ & C are inputs.

a$)$ Design and draw a logic circuit for $F$ by using a $74138$ Decoder and additional logic gates. Use logic template and label all inputs and outputs.

Table P$1$

$\backslash$table$[[A,B,C,F$