so I'm doing some predicate logic and I've stumbled upon a little confusion.
$∀c(R(c) \implies Y(c))$
Therefore: $\neg R(z)$
I don't understand how that works. What I do know, is that if $Y(z)$ is false, then yes, $R(z)$ must also be false, because there is no case where $R(z)$ is true and $Y(z)$ is false. But, there is a "for all c" quantifier there, doesn't that mean that for all inputs, $R(c)$ holds and so it must be true? I don't really understand, I might have read the definition of a quantifier the wrong way.
Help is much appreciated, thanks in advance!