Express logic and with +,-,*

Question

How can a logic and be expressed using only the arithmetic operators $+,-,*$ on $\{0,1\}$, taking $1 = $ True? To be precise: What function that uses only $+,-,*$ is $1$ when both arguments are $1$ and is $0$ otherwise for elements of $\{0,1\}$?

Answer 1

Since negation and conjunction form a functionally complete set of Boolean operators, it suffices to implement them. Take: \begin{align*} \textsf{Negation}(x) &= 1 - x \\ \textsf{Conjunction}(x, y) &= x \cdot y \end{align*}