$(15$ points$)$ A digital circuit accepts binary$-$coded$-$decimal $($BCD$)$ inputs $($cor only the numbers from $0_{10}$ to $9_{10}).$ The numbers are encoded using $4$ bits $A,$ is the MSB input bit and $D$ is the LSB input bit. The output $M$ is High $($logic $1$ equivalent of the input is NOT a multiple of $3($divisible by $3$ without a remair numbers greater than $9_{10}$ the output is zero.

a$.$ Show the complete truth table for this function

b$.$ Write the Sum$-$of$-$Products