I'm trying to write an equation to say: if $f(a)$ is greater than $f(b)$ for all the values of $b$, then $X$ is true. I figured the key here was the "all", so i tried to write it out using "for all" quantifier:
$\forall b, f(a)>f(b) \Rightarrow X$
However, $X$ should be true only if all the inequalities are true, and the above makes it look like $X$ can be true for any number of $b$. Is there an "aggregation" symbol suitable for a number of Boolean expressions so that I can draw just one conclusion? Alternately, would it be convenient to describe the maximum of the values of $f(b)$?
$(\forall b,f(a)>f(b))\Rightarrow X$