# Proving a tautology using truth table

• MarcL
In summary, the conversation is about proving whether a given statement is a tautology, contingency, or contradiction using a truth table. The statement in question is ((p_r)^(q_r))<-->((p^q)_r), and the individual is unsure of what to compare in order to make a determination. They later figure out that the statement is a tautology if the left-hand side of the bi-conditional is equal to the right-hand side. They also briefly discuss the symbols ^ and _ being used for conjunction and inclusive or, respectively. However, the individual also mentions that different symbols may be used in different fields or schools.

## Homework Statement

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

## 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!

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?

DEvens
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 ∧ ∨ ⊃ ⋅ ∴