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(pr)(st)
p
 t
1. (pr)(st) Premise
2. p Premise
3. pr 2, Addition
4. st 1, 3 Modus Ponens
5. t 4, Simplification

I am not getting two rules 1. addition (p→(pr))

                                         2. Simplification ((st)→t)

How and where we can apply?

in Mathematical Logic edited by
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Whenever there is an implication, try making the RHS false and LHS true. You cannot do it for the above 2 rt? That means the above 2 are tautology. Where we can apply? - Can be directly asked in a question or in form of English sentences.
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1. disjunctive syllogism

2. elimination

You may want to refer to this: https://www.tjhsst.edu/~rlatimer/ai/Logic/logicTable/node1.html

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