How do you convert these sentences into logic? Are these valid or invalid arguments and why?

LSAT Determined

Hello,

What logic form are these? ? And how would you translate this into logic as well as obtain its contrapositive?

I will run for office or I will shut my mouth. I ran for office. Thus, I didn't shut my mouth

If I am literate, then I can read and write. I can read but I can't write. Thus I am not literate

Accounts Playable

"Or" rules can be sometimes confusing since the English language is sometimes vague about inclusiveness or exclusiveness. Unless explicitly stated by the LSAT, always assume the inclusive or.

1.) Not run for office----->I shut my mouth. Contapositive: Not shut my mouth--->run for office. I ran for office (so we affirm the necessary condition; rule irrelevant). We cannot conclude that I didn't shut my mouth; this argument is invalid. Also, in this scenario, since we are assuming inclusive or, it is possible to both shut my mouth and run for office.

2.) I am literate--->I can read and I can write. Contrapositive: I cannot read or I cannot write--->I am not literate. I can read: this just affirms one element of the necessary condition, so we cannot conclude anything. I cannot write: here we know something. This is one of the sufficient conditions in the contrapositive. Thus, you must conclude that you are not literate. This argument is valid.

Link to the first "or" lesson: http://7sage.com/lesson/why-is-or-so-confusing/

Hope this helps!

nye8870

Nice explanation @"Accounts Playable" ! I would just add this: When the LSAT means for an "or" statement to exclusive, it will appear as "either x or y, but not both" which gets you a logical conversion of x <--> /y. The contrapositive of course is y <--> /x. These become very important in LG such as In/Out because then you know either x or y must be in, without the possibility of both In.