# How do you represent basic arithmetic using boolean function? [closed]

Say you have an arithmetic problem involving two variables, how do you give a Boolean formula for that using standard techniques so that one gets a minimal formula for a given number of quantifiers?

Consider for example a function that decides if $(1)$ $x>y$ or $(2)$ a function that decides $x|y$?

## closed as unclear what you're asking by D.W.♦, David Richerby, Juho, Jake, Nicholas MancusoMay 5 '15 at 1:07

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Hint: how do you add in elementary school? – Raphael Dec 7 '14 at 10:59
• Probably this is a stupid question. But curious about quantifier elimination. – Turbo Dec 7 '14 at 11:44

I assume you do know how to write a boolean circuit to test whether $x>y$. If not, consult a textbook.
• Thank you. Actually I 'know' does not mean I am comfortable using quantifiers. Is there a reference? I am thinking there is both a $\forall\exists$ and a $\exists\forall$ version. – Turbo Dec 7 '14 at 21:34