ranslate 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 unimpor$-$

tant 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 propo$-$

sitional variables; you should capture the negation in your translation using $.$

$($a$)$ I had good intentions and the highest hopes