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Math Help - Using "addition" Rules of inference

  1. #1
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    Using "addition" Rules of inference

    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?
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  2. #2
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    Re: Using "addition" Rules of inference

    Quote Originally Posted by Aquameatwad View Post
    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 Originally Posted by Aquameatwad View Post
    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).
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    Re: Using "addition" Rules of inference

    the "((p) and (q)) -> (p and q)" is exactly how my textbook defines a conjunction
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    Re: Using "addition" Rules of inference

    Quote Originally Posted by Aquameatwad View Post
    the "((p) and (q)) -> (p and q)" is exactly how my textbook defines a conjunction
    What textbook are you using?

    How does the textbook define the symbol (p)?

    The problem is with authors of logic textbooks. Each can have a different way of naming operations as well as different definitions.
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