Plese answer ALL parts of the question! $1.$ Boolean Algebra

Consider the following boolean formula in $4$ variables, A$,$ B$,$ C$,$ and D:

F$($A$,$B$,$C$,$D$)=($A$+$C$)($A$+$B$+$C$)($A$+$C$+$D$)($B$+$C$+$D$)$

a$.$ Compute the truth table for the given boolean formula.

b$.$ Find the min term expression. Name the terms.

c$.$ Find the max term expression. Name the terms.

d$.$ Create a Karnaugh map for the formula.

e$.$ Find the minimum Sum of Products $($SOP$)$ form from the Karnaugh map.

f$.$ Find the minimum Product of Sums $($POS$)$ form from the Karnaugh map for the complement of F$.$

g$.$ Draw the circuit diagram for the boolean formula using AND, OR$,$ and NOT gates.

h$.$ Draw the circuit diagram using only NAND gates.

i$.$ Implement F using a decoder.

j$.$ Implement F using an $8-$to$-1$ Multiplexer.