Question

Can somebody explain to me the following logical proposition?

Answer 1

\[(p \wedge q) \rightarrow (\neg p \veebar q)\] is a tautology?

Answer 2

On the left symbol I'm unfamiliar with that symbol, is that supposed to be a "nor"?

Answer 3

The reason I'm asking is it could also be considered an "xor" which is exclusive "or" (usually "or" is inclusive if both are true) and "nor" is really just the negation of the inclusive "or".

I added more quotations to make it readable since seeing "or" as a word is easier than to see that I mean it as an operator.

Answer 4

Alright I looked it up, and it is indeed xor. http://en.wikipedia.org/wiki/List_of_logic_symbols

So what exactly do you want explained about this? Are you trying to find a way to see if it is a tautology or are you trying to understand the meaning in words why this is a supposedly true statement?

Answer 5

Well I just worked it out, it's definitely a tautology, meaning it's always true. I guess if you need help in seeing why I'll be here for a while. I suggest setting up a truth table or something.

Answer 6

If it helps, you may think of \(\neg p \oplus q\) as \(\overline {p\oplus q}\)

xnor is true only when both \(p\) and \(q\) have the same truth value