How Do I Prove This Tautology?

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AI Thread Summary
The discussion centers on proving the tautology [(p or r) & (not(p) or r)] ---> r without using truth tables. The original poster expresses difficulty in simplifying the expression and seeks a more straightforward method. They initially struggle with the complexity of expanding terms but later find that distributing the implication leads to a quicker solution. Ultimately, they successfully solve the problem and share their approach. The thread highlights the importance of exploring different methods in logical 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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