A combinational logic circuit which has one output $Z$ and $4-$bit input ABCD

representing a binary number. $Z$ should be $1$ if and only if the input ABCD represents

a number between $0$ and $6($ABCD $=0000,0001,$dots,$0110).$ What is the minimum

solution for $Z(A,B,C,D)$ given in sum$-$of$-$product?

$Z(A,B,C,D)=A^{\text{'}}{C}^{\text{'}}+A^{\text{'}}{B}^{\text{'}}+A^{\text{'}}{D}^{\text{'}}$

$Z(A,B,C,D)=A^{\text{'}}BD+A{B}^{\text{'}}{D}^{\text{'}}+A{B}^{\text{'}}{C}^{\text{'}}+B^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$

$Z(A,B,C,D)=A^{\text{'}}{C}^{\text{'}}+A^{\text{'}}{B}^{\text{'}}+A^{\text{'}}C{D}^{\text{'}}$

Both options $1)$ and $3)$

None of the above