Logic: (p implies q) or (q implies r)

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Homework Help Overview

The original poster is studying natural deduction and is tasked with proving the logical expression (p implies q) or (q implies r). The context involves understanding logical implications and potentially tautologies.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the nature of the proof, questioning whether the original poster needs to simplify or expand the expression. There is mention of using the Law of Excluded Middle and the concept of tautologies, with suggestions to construct a truth table.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and the requirements for the proof. Some guidance has been offered regarding the use of truth tables, but no consensus has been reached on the approach to take.

Contextual Notes

There is a lack of premises provided in the original statement, which has led to confusion among participants regarding the nature of the proof required.

sombrancelha
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Homework Statement


I've started studying natural deduction recently and I have to prove

(p implies q) or (q implies r)

Homework Equations


--


The Attempt at a Solution


I thought about using the Law of Excluded Middle, but I'm not sure.
 
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isn't that only one side of an expression - what do you have to prove?
 
That's what I have to prove. There are no premisses.
 
could just be me, but still not getting it... usuallly you have something like, "knowing A, prove B" but you just have B?

do you mean you need to simplify or expand the expression?
 
I believe that you are supposed to show that the given expression is a tautology. IOW, an expression that is true for all values of p, q, and r. A simple way to do this is to make a truth table with 8 rows, one for each of the possible truth values for p, q, and r.
 

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