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?