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Is this true?

$$ \bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p_{i,j,n} \Longleftrightarrow \bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p_{(i,j,n)} \Longleftrightarrow \bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n) $$

vasili111
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    To me, yes. It's just a different notation for the indices, that's all. – b00n heT Sep 05 '18 at 16:59
  • You have to define your terms for us to be able to answer that. While b00n heT is right that all of those notations can be used as a way to index a collection of things, in this case propositions, it is unlikely all of them would be used simultaneously as synonyms. In that case, it is not necessarily the case that they are logically equivalent, or, more likely, that all of them are even well-formed formulas. At any rate, you can use whatever notation you like to index things as long as you define it. – Derek Elkins left SE Sep 05 '18 at 18:12
  • @DerekElkins Middle formula is from SAT solver from a discrete math book. I asked questions about it and one answer ( https://math.stackexchange.com/a/2893114/41724 ) was as in form of a formula on the left. The right formula is just my guess that I wanted to find out. – vasili111 Sep 05 '18 at 18:18

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