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I'm trying to prove that from P we can conclude that Q implies (P and Q). I understand how this is true intuitively, but I'm just getting a grasp of how to use propositional logic, its rules, etc. to express that. Any help would be appreciated. Also, how do I write propositional logic symbols on this site?

(1) P Premise
(2) Q Premise
(3) P and Q 1,2 And Introduction
(4) Q ⇒ (P and Q) 2,3 CP

Conifold
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Josh Boulton
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    Different systems use different conventions for predicate calculus, so you should settle on some textbook and follow it. This site does not process Latex, so you have to use html symbols, they can be copy-pasted from Wikipedia's list, for example. Also, to make a line break you either need to skip the next line or put
    at the end.     – Conifold Dec 04 '19 at 00:28
  • P => (Q => (P and Q)) is the formal statement of what you're trying to show, just FYI –  Dec 04 '19 at 16:44

1 Answers1

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Yes, that is basically it.

Premises are the undischarged assumptions. Here the second line is latter discharged; so it is just an Assumption.

In Fitch style proof presentation, it is helpful to mark contexts of assumptions as they are raised and discharged; this is usually done by some form of indentation.

|__(1) P               Premise 
|  |__(2) Q            Assumption 
|  |  (3) P ∧ Q        1,2 And Introduction (Conjunction Introduction)
|  (4) Q → (P ∧ Q)     2,3 CP (Conditional Introduction)

P ⊢ Q → (P ∧ Q)

As Conifold comments, you can find symbols to copy on https://en.wikipedia.org/wiki/List_of_logic_symbols

Graham Kemp
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