$1.($Total points $=20)$ Use symbols to write the logical forms of each of the following arguments.

Then prove whether the arguments are valid or invalid using rules of inference. For invalid

arguments, give a case that shows its invalidity.

$($a$)$ The domain is the set of students at an elementary school.

Every student who has a permission slip can go on the field trip.

Every student has a permission slip.

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$$ Every student can go on the field trip.

$($b$)$ The domain is the set of students at a university.

Larry is a student at the university.

Hubert is a student at the university.

Larry and Hubert are taking Boolean Logic.

Any student who takes Boolean Logic can take Algorithms.

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$$ Larry and Hubert can take Algorithms.