For any integers $m$ and $n$, if $7m+5n=147$, then $m$ is odd or $n$ is odd.
$$Q(m,n) \equiv 7m+5n=147$$
$$∀m∀n: Q(m,n) → \bigl(m \not\equiv 0 \!\!\pmod 2 \lor n \not\equiv 0 \!\! \pmod 2\bigr)$$
Am I right in assuming $\forall$ means "any" in this case? It doesn't seem to make sense to me ($\exists$ to me means "at least one, many, one, all but one, etc; anything less than all but more than none"), but Wikipedia states that $\forall$ can also mean "for any".
Is this correct?