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Proving a tautology using truth table

  1. Feb 3, 2015 #1
    1. The problem statement, all variables and given/known data
    ((p_r)^(q_r))<-->((p^q)_r) Prove whether the following statement is a tautology , contigency or contradiction using a truth table.

    2. Relevant equations


    3. 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!
     
  2. jcsd
  3. Feb 3, 2015 #2
    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?
     
  4. Feb 3, 2015 #3
    Well I used ^ for conjunction ( so AND) and _ for inclusive or because I can't the the opposite of ^ :) ( it was my own guess)
     
  5. Feb 3, 2015 #4
    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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