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Proving that $a⊢b$ if and only if $a⇒b$ is a tautology
0
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On my university exam paper there was a problem which description was the following:
Prove the following assertion: $a⊢b$ if and only if $a⇒b$ is a tautology.
How can I prove it?
logic propositional-calculus
edited Jan 5 at 8:54
Mauro ALLEGRANZA
65.1k448112
asked Jan 5 at 8:33
Dimitris PrasakisDimitris Prasakis
32
$endgroup$
|
show 3 more comments
0
$begingroup$
On my university exam paper there was a problem which description was the following:
Prove the following assertion: $a⊢b$ if and only if $a⇒b$ is a tautology.
How can I prove it?
logic propositional-calculus
edited Jan 5 at 8:54
Mauro ALLEGRANZA
65.1k448112
asked Jan 5 at 8:33
Dimitris PrasakisDimitris Prasakis
32
$endgroup$
$begingroup$
What have you tried ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
What is your proof system ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
See Soundness and completeness of the propositional calculus.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:56
$begingroup$
@MauroALLEGRANZA What do you mean what is my proof system?
$endgroup$
– Dimitris Prasakis
Jan 5 at 9:40
$begingroup$
What does it mean for you "$a vdash b$" ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 9:52
|
show 3 more comments
0
0
0
$begingroup$
On my university exam paper there was a problem which description was the following:
Prove the following assertion: $a⊢b$ if and only if $a⇒b$ is a tautology.
How can I prove it?
logic propositional-calculus
edited Jan 5 at 8:54
Mauro ALLEGRANZA
65.1k448112
asked Jan 5 at 8:33
Dimitris PrasakisDimitris Prasakis
32
$endgroup$
On my university exam paper there was a problem which description was the following:
Prove the following assertion: $a⊢b$ if and only if $a⇒b$ is a tautology.
How can I prove it?
logic propositional-calculus
logic propositional-calculus
edited Jan 5 at 8:54
Mauro ALLEGRANZA
65.1k448112
asked Jan 5 at 8:33
Dimitris PrasakisDimitris Prasakis
32
edited Jan 5 at 8:54
Mauro ALLEGRANZA
65.1k448112
asked Jan 5 at 8:33
Dimitris PrasakisDimitris Prasakis
32
edited Jan 5 at 8:54
Mauro ALLEGRANZA
65.1k448112
edited Jan 5 at 8:54
Mauro ALLEGRANZA
65.1k448112
edited Jan 5 at 8:54
Mauro ALLEGRANZA
65.1k448112
65.1k448112
asked Jan 5 at 8:33
Dimitris PrasakisDimitris Prasakis
32
asked Jan 5 at 8:33
Dimitris PrasakisDimitris Prasakis
32
asked Jan 5 at 8:33
Dimitris PrasakisDimitris Prasakis
32
32
$begingroup$
What have you tried ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
What is your proof system ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
See Soundness and completeness of the propositional calculus.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:56
$begingroup$
@MauroALLEGRANZA What do you mean what is my proof system?
$endgroup$
– Dimitris Prasakis
Jan 5 at 9:40
$begingroup$
What does it mean for you "$a vdash b$" ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 9:52
|
show 3 more comments
$begingroup$
What have you tried ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
What is your proof system ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
See Soundness and completeness of the propositional calculus.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:56
$begingroup$
@MauroALLEGRANZA What do you mean what is my proof system?
$endgroup$
– Dimitris Prasakis
Jan 5 at 9:40
$begingroup$
What does it mean for you "$a vdash b$" ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 9:52
$begingroup$
What have you tried ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
What have you tried ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
What is your proof system ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
What is your proof system ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
See Soundness and completeness of the propositional calculus.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:56
$begingroup$
See Soundness and completeness of the propositional calculus.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:56
$begingroup$
@MauroALLEGRANZA What do you mean what is my proof system?
$endgroup$
– Dimitris Prasakis
Jan 5 at 9:40
$begingroup$
@MauroALLEGRANZA What do you mean what is my proof system?
$endgroup$
– Dimitris Prasakis
Jan 5 at 9:40
$begingroup$
What does it mean for you "$a vdash b$" ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 9:52
$begingroup$
What does it mean for you "$a vdash b$" ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 9:52
|
show 3 more comments
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$begingroup$
What have you tried ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
What is your proof system ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:55
$begingroup$
See Soundness and completeness of the propositional calculus.
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 8:56
$begingroup$
@MauroALLEGRANZA What do you mean what is my proof system?
$endgroup$
– Dimitris Prasakis
Jan 5 at 9:40
$begingroup$
What does it mean for you "$a vdash b$" ?
$endgroup$
– Mauro ALLEGRANZA
Jan 5 at 9:52