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# Rules of inference and equivalence question?

Update:

s v r Premise

p Premise

r -> ~q Premise

p -> q Premise

Prove: s v t

I was able to do the harder ones but not this one and its supposedly the easiest...

### 1 Answer

Relevance

- SamwiseLv 75 years agoFavorite Answer
Using this reference set of rules of inference:

http://www.mathpath.org/proof/proof.inference.htm

1. S v R

2. P

3. R -> ~Q

4. P -> Q

5. Q [4 and 1, modus ponens]

6. ~R [3 and 5, modus tollens]

7. R v S [1, commutation]

8. S [7 and 6, disjunctive syllogism]

9, S v T [8, addition]

You can count on the addition rule coming into play when you see a variable that wasn't anywhere in the premises.

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