Can a minimal representation of a Boolean Function be 1 or 0

Question

After using the Karnaugh map to find the minimal representation of a Boolean function, my answer is 1.

Is 1 a valid answer for minimal representation?

If yes, what is the implication of a Boolean function has 1 as its minimal representation?

Answer 1

You are correct to find that $((x'y')(yz))'$ has minimal representation $1$ (which means the output is always $1,$ no matter the values of $x,y$ or $z$). To see this, note $(x'y')(yz)$ always outputs $0$, since $x'y'$ requires $y$ to be $0$ to output $1$ and $yz$ requires $y$ to be $1$ to output $1$, and you can't have both of those at the same time. Since $(x'y')(yz)$ always outputs $0,$ $((x'y')(yz))'$ always outputs $1.$