Translate the following English sentences into propositional formulas. Remember to define what your propositional variables mean!

For example, if the sentence was "The subject passed test $1$ and test $2.",$ a good answer might look like this:

$P$ : The subject passed test $1.$

$Q$ : The subject passed test $2.P^{{?}^{?}}Q$

Note that your propositional variables must be defined as complete propositions, so you should not just write:

$P$ : test $1$

$Q$ : test $2$

$P^{{?}^{?}}Q$

Sometimes $($like in this case$),$ it is necessary to slightly paraphrase so that your definitions are complete sentences.

Feel free to use abbreviations $($e$.$g$.,"$P: The subj. passed test $1.")$ or to omit unimportant words $($e$.$g$.,"Q$ : Subj. passed test $2.")$ if you're feeling lazy.

Words like "not", $"$no$",$ or "doesn't" should not appear in the definitions of your propositional variables; you should capture the negation in your translation using not.