SOLUTION: This question is about disjunctive argument. Please help. Identify whether the following disjunctive arguments are valid or invalid. Provide a reason for your answer. (a) Eit

Question 1062819: This question is about disjunctive argument. Please help.
Identify whether the following disjunctive arguments are valid or invalid. Provide a reason for your answer.
(a)
Either you like mathematics or you do not
You do not like physics
Therefore you can't say that you do.
(b)
Either you like mathematics or you do not
You do like mathematics
Therefore, you can't say that you do not.
I have no problem in logic especially on disjunctive arguments, but I have problems in understanding the conclusions of the arguments above because they sound ambiguous to me.
Thank you in advance for noticing and answering my problem.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Both are valid.

First argument: The first premise is irrelevant. But even if there are many shades of gray about your feelings about physics, "like" physics is only one of those shades, and "do not like" physics is all of the other shades, but "do not like" clearly excludes "like". Hence the statement "You like physics" following the premise "You do not like physics" would be false. ~p -> ~(~~p)

Second argument: The same logic applies, except that you don't have the problem of considering the "shades of gray" issue since the first premise defines only two possible feelings about physics; like or don't like. Again, the statement "You do not like mathematics" following the premise "You do like mathematics" would be false. p -> ~(~p)

John

My calculator said it, I believe it, that settles it

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