Inferring P from P v Q': Is it Valid?

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SUMMARY

The discussion centers on the validity of inferring P from the expression P v Q'. It is established that one cannot infer P directly from P v Q, as the logical structure does not support this conclusion. The participants clarify that while P can be assumed, it must be validated through proof. Additionally, it is confirmed that from the conjunction P & Q, P can be inferred, and similarly, P can be inferred from P & Q' if Q' represents not-Q.

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  • Understanding of propositional logic and inference rules
  • Familiarity with logical operators, specifically "OR" (v) and "AND" (&)
  • Knowledge of proof techniques in formal logic
  • Concept of negation in logical expressions
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  • Study the rules of inference in propositional logic
  • Learn about the implications of logical conjunctions and disjunctions
  • Explore proof techniques, including direct proof and proof by contradiction
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Students of logic, mathematicians, and anyone interested in formal reasoning and proof validation in propositional logic.

EvLer
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So, there is this "inference rule" in my textbook:
from P v Q, we can assume P

but does this hold for P v Q', i.e. given this, can I say we have P?

My intuition says "no", but I'd rather have a reasoned answer...
Thanks in advance.
 
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From P v Q, you may not infer P. You can assume P anytime you like, so long as you discharge all assumptions by the end of your proof. By "v", you do mean "OR", right? From P & Q you certainly may infer P. And if, by Q' you mean not-Q, then you may infer P from P & Q' just as you may infer it from P & Q.
 

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