Help, using Truth Table prove that the following logic statement is a Tautologyby Tek1Atom Tags: engineering, logic, philosophy, tautology, truth table 

#1
Aug3010, 01:15 PM

P: 15

1. The problem statement, all variables and given/known data
By providing a truth table, show that the following logic statement is a tautology: p ∧ (p → q) → q Any help will be much appreciated. Thank You 



#2
Aug3010, 02:19 PM

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I would set up a truth table with columns for p, q, and p ==> q. You know how many rows you need, right?




#3
Aug3010, 07:36 PM

P: 15

p  q  P → q
 T  T  T T  F  F F  T  T F  F  T Thank you Mark44 but I don't think this is the correct answer/method as the output has to be true in all cases in order for it to be labeled a tautology. Any other suggestions? 



#4
Aug3010, 07:48 PM

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P: 14,433

Help, using Truth Table prove that the following logic statement is a Tautology
You are missing at least one column, multiple columns if you want to break things down.




#5
Aug3010, 07:51 PM

P: 15

D H could you give me an example please as I am new to logic...




#6
Aug3010, 08:10 PM

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P: 14,433

You have the truth table for implication. p→q obviously is not a tautology. You weren't asked to show that. You were asked to show that p∧(p→q)→q is a tautology. Your truth table needs to end with a p∧(p→q)→q column on the right and with all four values in this column being T.




#7
Aug3110, 04:09 PM

P: 15

Thank you DH, that was very helpful. My final question is, does it matter which way we write down the truth table?
e.g. which one is correct? p  q  P → q  p∧(p→q)→q  T  T  T  T T  F  F  T F  T  T  T F  F  T  T OR p  q  P → q  p∧(p→q)→q  F  F  T  T F  T  T  T T  F  F  T T  T  T  T 



#8
Aug3110, 05:11 PM

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P: 14,433

You aren't going to get points for that. At least I hope you aren't. There is a thing called showing your work.




#9
Aug3110, 06:05 PM

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P: 20,962





#10
Aug3110, 06:08 PM

P: 15

Thank You Mark44. You have been great!



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