Multiple logical quantities for English statement? Express each of the following statements as a conditional statement in "if-then" form or as a universally quantified statement. Also write the negation (without phrases like "it is false that") 
g) I get mad whenever you do that. 
Here's the answer I've found, and why I'm confused as to exactly why it's the way it is. 
g) I get mad whenever you do that. 
let $P(x)$ mean "I get mad"
let $Q(x)$ mean "you do that" 
$\forall x Q(x)(P(x))$
the negation of this is $\exists x Q(x)(\lnot P(x))$
Sometimes you do that and I don't get mad. 
I can see how this line or reason works. But why can't it be phrased as follows? 
If you do that then I get mad. 
$Q(x) \rightarrow P(x)$ or equivalently $\lnot Q(x) \lor P(x)$
the negation is then $ Q(x) \land \lnot P(x)$
You do that and I don't get mad. 
These can't be the same thing, can they? Sometimes I don't get mad isn't the same thing as I don't get mad. Can someone explain why it's the first result, and not the second? 
 A: The original statement uses "whenever", so implicitly it's saying something about all "times", that is, "occasions". $x$ ranges over "times", "occasions" – times when the other person does that, times when you get mad.
So: 
let $P(x)$ mean "I get mad at (or a little after) time x", and
let $Q(x)$ mean "you do that at time x". 
Then "I get mad when you do that" is representable as:
$$ \forall x(Q(x) \implies P(x))$$
so its negation is:
$$ \exists x(Q(x) \wedge \neg P(x))$$
or, in English, "Sometimes you do that and I don't get mad" (really we'd say "but I don't get mad"), or still more idiomatically "I don't always get mad when you do that".
Your alternative, "If you do that then I get mad", doesn't explicitly mention "times" but it's phrased as a rule, a tenseless statement true for all times. You propose representing it as 
$$Q(x) \implies P(x)$$ 
without an explicit quantifier, but then: what is $x$ supposed to be?? If you think $x$ is superfluous then just try using mere propositional variables: 
$$Q \implies P \tag{*}$$
You can't faithfully model the original statement that way, because (*) loses "whenever", "for all occasions x".
Here, $Q$ is supposed to be "You do that", but in what sense? As a one-shot event? all the time? Similarly, $P$ means "I get mad", but in what sense? Once? All the time? Every Tuesday? Whichever of these meanings you assign to $P$ and $Q$, (*) doesn't mean what the original statement does.
A: The problem is that $Q(x) \rightarrow P(x)$ is not a complete sentence: we use the variable $x$ without introducing it. 
A more proper rendering of "If you do that then I get mad." would be $\forall x:Q(x)\rightarrow P(x)$, or equivalently $\forall x:\lnot Q(x) \lor P(x)$. Its negation then becomes $\exists x: Q(x) \land \lnot P(x)$, or in words "There is a case where you do that and I don't get mad."
A: Your propositional logic statements should be written without the entity: $Q\to P$ and $Q\wedge\neg P$ .   Propositions are considered to be invariant.   They are held to be either true or false.
You predicate logic statements can also be written as: $\forall x\big(Q(x)\to P(x)\big)$ and $\exists x\big(Q(x)\wedge\neg P(x)\big)$ .   The truth of a predicate may be dependent on the state of a variable.
The difference between the predicate logic statements and the propositional logic statement is entirely: the quantifiers and the variable entity.   That is the added semantics of "always" and "sometimes".
