Deduce P from Sigma { ~S V R, R -> P, S }

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In summary, the conversation discusses a deduction with the component P. The attempt at a solution involves showing that Sigma implies P, which is proved as a tautology. The deduction follows a straightforward process, using modus ponens and exportation.
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moo5003
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Homework Statement


Sigma = { ~S V R, R -> P, S }

Give a deduction with the last component P.

The Attempt at a Solution



I came up with what I think is an answer, but I was a little unsure on what can go in a deduction so I would really like someone to re-check and tell me if I'm right and if not what rules I broke.

<R->P, S, (~SVR)->R, ~SVR, R, P>

R->P is in Sigma
S is in Sigma
(~SVR)->R is a tautology since R always implies R and S is listed before making it always True.
~SVR is in sigma
R by modus ponus.
P by modus ponus.

Is this correct?

Another version I have after doing subsequent problems is this:

First: I showed that Sigma Implies P.

Thus the following is a tautology
(~SVR)->(R->P)->S->P = B

then the deduction looks like:
<B,~SVR,(R->P)->S->P,R->P,S->P,S,P>

1st Term is a tautology
2nd Term in sigma
3rd Term modus ponus
4th Term in sigma
5th Term modus ponus
6th Term in sigma
7th Term modus ponus

This seems a lot more straightforward since I was a little unsure about the (~SVR)->R since its not really a tautology unless you assume ~S is always false ie: S is always true.

The 1st term B isn't that hard to prove as a tautology since if Sigma implies P then the wff's in conjuction form a tautology when if wff's then P and then you can use exportation on it to distribute the conjuctions to if/thens for each term.
 
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I like it. It should work.
 
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FAQ: Deduce P from Sigma { ~S V R, R -> P, S }

What is the meaning of "Deduce P from Sigma { ~S V R, R -> P, S }"?

The phrase "deduce P from Sigma { ~S V R, R -> P, S }" is an expression used in logic and mathematics. It represents a logical deduction, where P is the conclusion and Sigma { ~S V R, R -> P, S } is the set of premises or assumptions.

How do you deduce P from Sigma { ~S V R, R -> P, S }?

Deducing P from Sigma { ~S V R, R -> P, S } requires using logical reasoning and applying rules of inference, such as modus ponens and modus tollens. This involves examining the premises and using them to logically derive the conclusion.

What does ~S V R mean in "Deduce P from Sigma { ~S V R, R -> P, S }"?

The symbol ~S V R represents the logical statement "not S or R," also known as a disjunction. This means that at least one of the two statements, ~S or R, must be true for the entire statement to be true. In this context, it is one of the premises in the set Sigma.

Can you provide an example of deducing P from Sigma { ~S V R, R -> P, S }?

Yes, for example, if we have the premises ~S V R and R -> P, we can use modus ponens to deduce P. This is because if ~S V R is true, and R -> P is true, then P must also be true. Therefore, the conclusion P can be deduced from these premises.

What is the significance of "Deduce P from Sigma { ~S V R, R -> P, S }" in scientific research?

In scientific research, logical deductions are used to make conclusions based on evidence and data. The expression "Deduce P from Sigma { ~S V R, R -> P, S }" represents the process of using logical reasoning to derive a conclusion from a set of premises. This can help scientists make informed and accurate conclusions based on their research.

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