Question 972808
<font face="Times New Roman" size="+2">


I assume that your first example is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P\ \large \vee \LARGE\ Q]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \neg P]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \text{Therefore } Q]


This is valid by disjunctive syllogism.


I'm not sure what you mean by your second example.  If by "<>" you mean to indicate the biconditional (you should represent this by using "<->" or "iff"), then the argument is invalid.  Assume both P and Q are true, then the bi-conditional is true, but *[tex \Large \neg(T\ \large\vee\Large \neg T)] is false.  Hence *[tex \Large P\ \large\wedge\Large\ Q] is a possible counterexample.  If you meant something different than *[tex \Large P\ \Leftrightarrow\ Q] when you wrote P<>Q, then you are on your own.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \