How Do I Prove This Tautology?

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SUMMARY

The discussion centers on proving the tautology [(p or r) & (not(p) or r)] ---> r without using truth tables. The original poster initially struggled with simplification but ultimately found success by distributing the implication, which led to a quicker resolution. This approach emphasizes the importance of understanding logical implications and simplification techniques in propositional logic.

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  • Familiarity with logical operators such as "or", "not", and "implies"
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  • Basic knowledge of logical equivalences and simplification techniques
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  • Study methods for distributing logical implications in propositional logic
  • Learn about logical equivalences and their applications in proofs
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Homework Statement



[ (p or r) & (not(p) or r) ] ---> r is a tautology. Prove this without using truth tables.

Homework Equations



See above. not(p) = !p = p' = the opposite value of p and ---> is an implication.

The Attempt at a Solution



I have made some prior simplification, and that is what I have at present. I don't know where to go from here. Expanding the terms seems to make things too complicated. Is there a shorter way?

Any help would be greatly appreciated!
 
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Nevermind, I've solved it! For anyone interested in the solution, I just had to distribute the implication and then expanding was a lot quicker!
 

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