Question

For each argument determine whether it is valid or not and explain why (in a sentence).

(a)"Some math majors left the campus for the weekend" and "All seniors left the campus for the weekend" implies the conclusion "Some seniors are math majors."
(b)"Everyone who left campus for the weekend is a senior" and "All math majors left campus for the weekend" implies the conclusion "All math majors are seniors."
(c)"No juniors left campus for the weekend" and "Some math majors are not juniors" implies the conclusion "Some math majors left campus for the weekend."

Answer 1

In argument (a), the conclusion is not valid because the premises do not guarantee that some seniors are math majors. In argument (b), the conclusion is valid because the premises guarantee that all math majors are seniors. In argument (c), the conclusion is not valid because the premises do not provide enough information to support the conclusion that some math majors left campus for the weekend.

Step-by-step explanation:

In argument (a), it is not valid because the premises do not guarantee that some seniors are math majors. It is possible for seniors to leave campus for the weekend without being math majors.

In argument (b), it is valid because the premises guarantee that all math majors are seniors. If everyone who left campus for the weekend is a senior and all math majors left campus, then all math majors are seniors.

In argument (c), it is not valid because the premises do not provide enough information to support the conclusion that some math majors left campus for the weekend. There could be math majors who didn't leave campus or there could be other reasons why some math majors are not juniors.