Is it possible to test $x > c$ and $y > c$ using only one condition?

Question

Is it possible to test $x > c$ and $y > c$ using only one condition?

If it's not possible within $(-\infty,+\infty)$, is it possible in $[0,1]$ ?

Thanks,

Answer 1

You want to know if $\min\{x,y\}>c$.

We can write: $$\min\{x,y\} = \frac{x+y}2 - \frac{|x-y|}2$$

Now it is simple to verify if both $x,y$ are bigger than $c$ or not.

Answer 2

This is a job for universality

$\rm\: a < b,c \iff a < min\{b,c\}\ $

$\rm\: a\ \ |\ \ b,c \iff a\ \ |\ \ \gcd\{b,c\}$

$\rm\: a\subset b,c \iff a\subset \ b\ \cap\ c $