Question $13$

$5$ pts

Consider the following deduction problem to be coded and solved in propositional logic. The following propositions are used:

$\backslash$table$[[$Proposition$,$Meaning$],[$Study$,$True, if Study. False, otherwise.$],[$Do$-$well,True, if do well in exams. False, otherwise.$],[$Relax$,$True, If relax. False, otherwise.$],[$Enjoy$,$True, If enjoy. False, otherwise.$]]$

Write the following sentences in propositional logic without using the implication $(=>>$ operator, that is use only and $({?}^{{?}^{?}}),$ or$($v$)$ and not $()$ operators.

If I study then I do well in the examinations

If I relax then I enjoy myself $[$Select$].$

$$

Either I study or I relax but not both $$

If I study then I do not enjoy myself $$

If I relax then I do not do well in the exams $$

Goal: I enjoy myself if and only if I do not do well in the examinations can be expressed in propositional logic as $($Do$-$well $vv$ Enjoy$)^($ Enjoy v Do$-$well$)$