Proving a tautology using truth table

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Discussion Overview

The discussion revolves around the task of proving whether the statement ((p_r)^(q_r))<-->((p^q)_r) is a tautology, contingency, or contradiction using a truth table. Participants explore the methodology for constructing the truth table and the interpretation of logical symbols used in the statement.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about how to compare parts of the bi-conditional statement to determine its nature as a tautology, contingency, or contradiction.
  • Another participant inquires about the meaning of the symbols ^ and _, suggesting that different fields may use different notations.
  • One participant confirms their understanding that ^ represents conjunction (AND) and _ represents inclusive disjunction (OR), although they express uncertainty about the opposite of conjunction.
  • A later reply offers a suggestion to use a toolbar feature to access various logical symbols, indicating a resource for clarity in notation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the symbols used in the logical statement, as there are differing conventions mentioned. The initial confusion regarding the truth table construction also remains unresolved.

Contextual Notes

There is an indication of varying notation conventions among participants, which may affect their understanding of the logical statement. The discussion does not resolve the specific steps needed to construct the truth table or the criteria for determining the nature of the statement.

MarcL
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Homework Statement


((p_r)^(q_r))<-->((p^q)_r) Prove whether the following statement is a tautology , contigency or contradiction using a truth table.

Homework Equations

The Attempt at a Solution


I did the truth table, but this whole thing is one statement no? What do I compare? the first half of the bi conditional statement to the second? or the whole statement vs. the two halves? I don't know which to compare to decide whether or not it is a contingency.EDIT: figured out the tautology is if L.H.S of <--> is equal to RHS. Sorry for the post!
 
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Just a question for you, what is ^ and _? In the logic courses I took, we used different symbols and I'm aware different schools/fields use different symbols so just wanted to know what yours are. Thanks :)

Btw I'm guessing ^ is conjunction and _ is disjunction?
 
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Well I used ^ for conjunction ( so AND) and _ for inclusive or because I can't the the opposite of ^ :) ( it was my own guess)
 
MarcL said:
Well I used ^ for conjunction ( so AND) and _ for inclusive or because I can't the the opposite of ^ :) ( it was my own guess)

Ah, alright :D If you click the sigma Σ button on the toolbar, there are many symbols to choose from including ∧ ∨ ⊃ ⋅ ∴
 

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