Symbolic Logic: Helping a Friend Understand Mr. X's Homework

[buddyholly9999]

Ok..tried to help a friend understand some of his homework..I haven't seen symbolic logic since college, but there was this one problem in particular that went something like..."Mr. X got a C on his final." and "Mr. X passed the class"...we say that these are represented by p and q, respectively. Then it goes on to list some statements which you have to write in symbols.

1) Mr. X did not get a C on his final but he passed the class...
my response was ... ~p and q
I'm pretty damn sure I'm right but he kept complaining that the but might not denote the 'and' connective.

2) It was necessary for Mr. X to get a C on his final in order for him to pass the class.
My response was... q => p

3)
Mr. X passed the class only if he got a C on his final.
My response was... q => p

He trusts me that I'm right...and I'm figuring that the second and third responses are correct..but I'm worried I'm wrong..if you read the second and third statements, you can see why someone would think that they are essentially the same.

some feedback would be nice..even if it's to %^&^ off...:)

 

[AKG]

1) is correct, and "but" is always denoted by the "and" connective.
2) is correct.
3) is correct.