Mixing
Equivalent sets of wffs
$begingroup$
Propositional logic. Given two sets of wffs, $Sigma$ and $Gamma$, are the following definitions of equivalence between $Sigma$ and $Gamma$ .....equivalent?
$(SigmavDashGamma)land(GammavDashSigma)$
For all $alpha$, $(SigmavDashalpha)leftrightarrow(GammavDashalpha)$
I'm not looking for a proof, a just want to avoid engaging myself in a lost battle.
propositional-calculus
asked Jan 25 at 19:49
PeptideChainPeptideChain
464311
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add a comment |
$begingroup$
Propositional logic. Given two sets of wffs, $Sigma$ and $Gamma$, are the following definitions of equivalence between $Sigma$ and $Gamma$ .....equivalent?
$(SigmavDashGamma)land(GammavDashSigma)$
For all $alpha$, $(SigmavDashalpha)leftrightarrow(GammavDashalpha)$
I'm not looking for a proof, a just want to avoid engaging myself in a lost battle.
propositional-calculus
asked Jan 25 at 19:49
PeptideChainPeptideChain
464311
$endgroup$
add a comment |
$begingroup$
Propositional logic. Given two sets of wffs, $Sigma$ and $Gamma$, are the following definitions of equivalence between $Sigma$ and $Gamma$ .....equivalent?
$(SigmavDashGamma)land(GammavDashSigma)$
For all $alpha$, $(SigmavDashalpha)leftrightarrow(GammavDashalpha)$
I'm not looking for a proof, a just want to avoid engaging myself in a lost battle.
propositional-calculus
asked Jan 25 at 19:49
PeptideChainPeptideChain
464311
$endgroup$
Propositional logic. Given two sets of wffs, $Sigma$ and $Gamma$, are the following definitions of equivalence between $Sigma$ and $Gamma$ .....equivalent?
$(SigmavDashGamma)land(GammavDashSigma)$
For all $alpha$, $(SigmavDashalpha)leftrightarrow(GammavDashalpha)$
I'm not looking for a proof, a just want to avoid engaging myself in a lost battle.
propositional-calculus
propositional-calculus
asked Jan 25 at 19:49
PeptideChainPeptideChain
464311
asked Jan 25 at 19:49
PeptideChainPeptideChain
464311
asked Jan 25 at 19:49
PeptideChainPeptideChain
464311
asked Jan 25 at 19:49
PeptideChainPeptideChain
464311
asked Jan 25 at 19:49
PeptideChainPeptideChain
464311
464311
add a comment |
add a comment |
1 Answer
1
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$begingroup$
Two sets of formulas are equivalent, if any formula of the one set is a consequence of the other and conversely.
Equivalently, they have the same models.
This means :
$text {for every } alpha in Gamma : Sigma vDash alpha$ and $text { for every } beta in Sigma : Gamma vDash beta$.
answered Jan 25 at 19:57
Mauro ALLEGRANZAMauro ALLEGRANZA
67.3k449115
$endgroup$
$begingroup$
Is there any relation with the two expressions in the Q?
$endgroup$
– PeptideChain
Jan 25 at 20:12
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Two sets of formulas are equivalent, if any formula of the one set is a consequence of the other and conversely.
Equivalently, they have the same models.
This means :
$text {for every } alpha in Gamma : Sigma vDash alpha$ and $text { for every } beta in Sigma : Gamma vDash beta$.
answered Jan 25 at 19:57
Mauro ALLEGRANZAMauro ALLEGRANZA
67.3k449115
$endgroup$
$begingroup$
Is there any relation with the two expressions in the Q?
$endgroup$
– PeptideChain
Jan 25 at 20:12
add a comment |
$begingroup$
Two sets of formulas are equivalent, if any formula of the one set is a consequence of the other and conversely.
Equivalently, they have the same models.
This means :
$text {for every } alpha in Gamma : Sigma vDash alpha$ and $text { for every } beta in Sigma : Gamma vDash beta$.
answered Jan 25 at 19:57
Mauro ALLEGRANZAMauro ALLEGRANZA
67.3k449115
$endgroup$
$begingroup$
Is there any relation with the two expressions in the Q?
$endgroup$
– PeptideChain
Jan 25 at 20:12
add a comment |
$begingroup$
Two sets of formulas are equivalent, if any formula of the one set is a consequence of the other and conversely.
Equivalently, they have the same models.
This means :
$text {for every } alpha in Gamma : Sigma vDash alpha$ and $text { for every } beta in Sigma : Gamma vDash beta$.
answered Jan 25 at 19:57
Mauro ALLEGRANZAMauro ALLEGRANZA
67.3k449115
$endgroup$
Two sets of formulas are equivalent, if any formula of the one set is a consequence of the other and conversely.
Equivalently, they have the same models.
This means :
$text {for every } alpha in Gamma : Sigma vDash alpha$ and $text { for every } beta in Sigma : Gamma vDash beta$.
answered Jan 25 at 19:57
Mauro ALLEGRANZAMauro ALLEGRANZA
67.3k449115
answered Jan 25 at 19:57
Mauro ALLEGRANZAMauro ALLEGRANZA
67.3k449115
answered Jan 25 at 19:57
Mauro ALLEGRANZAMauro ALLEGRANZA
67.3k449115
answered Jan 25 at 19:57
Mauro ALLEGRANZAMauro ALLEGRANZA
67.3k449115
67.3k449115
$begingroup$
Is there any relation with the two expressions in the Q?
$endgroup$
– PeptideChain
Jan 25 at 20:12
add a comment |
$begingroup$
Is there any relation with the two expressions in the Q?
$endgroup$
– PeptideChain
Jan 25 at 20:12
$begingroup$
Is there any relation with the two expressions in the Q?
$endgroup$
– PeptideChain
Jan 25 at 20:12
$begingroup$
Is there any relation with the two expressions in the Q?
$endgroup$
– PeptideChain
Jan 25 at 20:12
add a comment |
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