# Using "addition" Rules of inference

• Feb 9th 2013, 06:10 PM
I have a question about using the addition rule of inference. I haven't seen many examples of its use so I'm wondering in what situations i would be able to use it in.
I know its "p-> (p or q)" so would i be able to use this as you would use a conjunction which is ((p) and (q)) -> (p and q)?

So if i have a "p" and i also have a "q" is it valid to say by addition p or q?
• Feb 10th 2013, 12:55 PM
emakarov
Re: Using "addition" Rules of inference
Quote:

I know its "p-> (p or q)" so would i be able to use this as you would use a conjunction which is ((p) and (q)) -> (p and q)?

I don't understand the difference between ((p) and (q)) an (p and q).

Quote:

So if i have a "p" and i also have a "q" is it valid to say by addition p or q?

Yes, and you can derive (p or q) from just p, or from just q.

This rule is needed, in particular, to derive commutativity of disjunction. Indeed, suppose (p or q). We are reasoning by cases. If p, then (q or p) by addition. Similarly, if q, then again (q or p). Since in both cases we have the same conclusion, this conclusion follows from (p or q).
• Feb 10th 2013, 04:07 PM
Re: Using "addition" Rules of inference
the "((p) and (q)) -> (p and q)" is exactly how my textbook defines a conjunction
• Feb 10th 2013, 04:17 PM
Plato
Re: Using "addition" Rules of inference
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