Propositional Logic Translation
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I am trying to convert the following into propositional logic in order to construct a semantic tableaux:
If Mark goes to the party, then so does Pat. John or Pat will go to
the party. John will not go to the party unless Steve goes to the party.
Steve does not go the party and neither does Mark. Therefore, Pat does
go to the party.
What I have gotten so far is $M implies P$, $J lor P$,$neg S land neg M$,$neg P$
I am not sure how to translate "John will not go to the party unless Steve goes to the party."
Thanks in advance for any help given!
logic propositional-calculus
asked Dec 18 '18 at 2:11
martinhynesonemartinhynesone
367
$endgroup$
add a comment |
$begingroup$
I am trying to convert the following into propositional logic in order to construct a semantic tableaux:
If Mark goes to the party, then so does Pat. John or Pat will go to
the party. John will not go to the party unless Steve goes to the party.
Steve does not go the party and neither does Mark. Therefore, Pat does
go to the party.
What I have gotten so far is $M implies P$, $J lor P$,$neg S land neg M$,$neg P$
I am not sure how to translate "John will not go to the party unless Steve goes to the party."
Thanks in advance for any help given!
logic propositional-calculus
asked Dec 18 '18 at 2:11
martinhynesonemartinhynesone
367
$endgroup$
1
$begingroup$
"Unless" means "if not".
$endgroup$
– David
Dec 18 '18 at 2:22
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So would it be !J implies !S?
$endgroup$
– martinhynesone
Dec 18 '18 at 2:28
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Thank you for the help!!
$endgroup$
– martinhynesone
Dec 18 '18 at 2:30
$begingroup$
@martinhynesone sorry, I had that wrong ... it ahould be $neg S rightarrow neg J$
$endgroup$
– Bram28
Dec 18 '18 at 2:31
add a comment |
$begingroup$
I am trying to convert the following into propositional logic in order to construct a semantic tableaux:
If Mark goes to the party, then so does Pat. John or Pat will go to
the party. John will not go to the party unless Steve goes to the party.
Steve does not go the party and neither does Mark. Therefore, Pat does
go to the party.
What I have gotten so far is $M implies P$, $J lor P$,$neg S land neg M$,$neg P$
I am not sure how to translate "John will not go to the party unless Steve goes to the party."
Thanks in advance for any help given!
logic propositional-calculus
asked Dec 18 '18 at 2:11
martinhynesonemartinhynesone
367
$endgroup$
I am trying to convert the following into propositional logic in order to construct a semantic tableaux:
If Mark goes to the party, then so does Pat. John or Pat will go to
the party. John will not go to the party unless Steve goes to the party.
Steve does not go the party and neither does Mark. Therefore, Pat does
go to the party.
What I have gotten so far is $M implies P$, $J lor P$,$neg S land neg M$,$neg P$
I am not sure how to translate "John will not go to the party unless Steve goes to the party."
Thanks in advance for any help given!
logic propositional-calculus
logic propositional-calculus
asked Dec 18 '18 at 2:11
martinhynesonemartinhynesone
367
asked Dec 18 '18 at 2:11
martinhynesonemartinhynesone
367
asked Dec 18 '18 at 2:11
martinhynesonemartinhynesone
367
asked Dec 18 '18 at 2:11
martinhynesonemartinhynesone
367
asked Dec 18 '18 at 2:11
martinhynesonemartinhynesone
367
367
1
$begingroup$
"Unless" means "if not".
$endgroup$
– David
Dec 18 '18 at 2:22
$begingroup$
So would it be !J implies !S?
$endgroup$
– martinhynesone
Dec 18 '18 at 2:28
$begingroup$
Thank you for the help!!
$endgroup$
– martinhynesone
Dec 18 '18 at 2:30
$begingroup$
@martinhynesone sorry, I had that wrong ... it ahould be $neg S rightarrow neg J$
$endgroup$
– Bram28
Dec 18 '18 at 2:31
add a comment |
1
$begingroup$
"Unless" means "if not".
$endgroup$
– David
Dec 18 '18 at 2:22
$begingroup$
So would it be !J implies !S?
$endgroup$
– martinhynesone
Dec 18 '18 at 2:28
$begingroup$
Thank you for the help!!
$endgroup$
– martinhynesone
Dec 18 '18 at 2:30
$begingroup$
@martinhynesone sorry, I had that wrong ... it ahould be $neg S rightarrow neg J$
$endgroup$
– Bram28
Dec 18 '18 at 2:31
1
1
$begingroup$
"Unless" means "if not".
$endgroup$
– David
Dec 18 '18 at 2:22
$begingroup$
"Unless" means "if not".
$endgroup$
– David
Dec 18 '18 at 2:22
$begingroup$
So would it be !J implies !S?
$endgroup$
– martinhynesone
Dec 18 '18 at 2:28
$begingroup$
So would it be !J implies !S?
$endgroup$
– martinhynesone
Dec 18 '18 at 2:28
$begingroup$
Thank you for the help!!
$endgroup$
– martinhynesone
Dec 18 '18 at 2:30
$begingroup$
Thank you for the help!!
$endgroup$
– martinhynesone
Dec 18 '18 at 2:30
$begingroup$
@martinhynesone sorry, I had that wrong ... it ahould be $neg S rightarrow neg J$
$endgroup$
– Bram28
Dec 18 '18 at 2:31
$begingroup$
@martinhynesone sorry, I had that wrong ... it ahould be $neg S rightarrow neg J$
$endgroup$
– Bram28
Dec 18 '18 at 2:31
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
A statement '$P $ unless $Q$' typically translates to '$P$ if not $Q$', i.e. $neg Q rightarrow P$
Here is an example:
'You fail ($F$) the course unless you complete ($C$) all the HW's'
OK, so if someone does not complete all the HW's they will clearly fail the course: $neg C rightarrow F$
Ok, but will you pass the course if you do complete all the HW's? No, not necessarily .. you may also have to do well on the final, for example. So, we cannot say $C rightarrow neg F$ ... so it is not a biconditional.
answered Dec 18 '18 at 2:52
Bram28Bram28
60.7k44590
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add a comment |
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$begingroup$
A statement '$P $ unless $Q$' typically translates to '$P$ if not $Q$', i.e. $neg Q rightarrow P$
Here is an example:
'You fail ($F$) the course unless you complete ($C$) all the HW's'
OK, so if someone does not complete all the HW's they will clearly fail the course: $neg C rightarrow F$
Ok, but will you pass the course if you do complete all the HW's? No, not necessarily .. you may also have to do well on the final, for example. So, we cannot say $C rightarrow neg F$ ... so it is not a biconditional.
answered Dec 18 '18 at 2:52
Bram28Bram28
60.7k44590
$endgroup$
add a comment |
$begingroup$
A statement '$P $ unless $Q$' typically translates to '$P$ if not $Q$', i.e. $neg Q rightarrow P$
Here is an example:
'You fail ($F$) the course unless you complete ($C$) all the HW's'
OK, so if someone does not complete all the HW's they will clearly fail the course: $neg C rightarrow F$
Ok, but will you pass the course if you do complete all the HW's? No, not necessarily .. you may also have to do well on the final, for example. So, we cannot say $C rightarrow neg F$ ... so it is not a biconditional.
answered Dec 18 '18 at 2:52
Bram28Bram28
60.7k44590
$endgroup$
add a comment |
$begingroup$
A statement '$P $ unless $Q$' typically translates to '$P$ if not $Q$', i.e. $neg Q rightarrow P$
Here is an example:
'You fail ($F$) the course unless you complete ($C$) all the HW's'
OK, so if someone does not complete all the HW's they will clearly fail the course: $neg C rightarrow F$
Ok, but will you pass the course if you do complete all the HW's? No, not necessarily .. you may also have to do well on the final, for example. So, we cannot say $C rightarrow neg F$ ... so it is not a biconditional.
answered Dec 18 '18 at 2:52
Bram28Bram28
60.7k44590
$endgroup$
A statement '$P $ unless $Q$' typically translates to '$P$ if not $Q$', i.e. $neg Q rightarrow P$
Here is an example:
'You fail ($F$) the course unless you complete ($C$) all the HW's'
OK, so if someone does not complete all the HW's they will clearly fail the course: $neg C rightarrow F$
Ok, but will you pass the course if you do complete all the HW's? No, not necessarily .. you may also have to do well on the final, for example. So, we cannot say $C rightarrow neg F$ ... so it is not a biconditional.
answered Dec 18 '18 at 2:52
Bram28Bram28
60.7k44590
edited Dec 19 '18 at 17:02
answered Dec 18 '18 at 2:52
Bram28Bram28
60.7k44590
answered Dec 18 '18 at 2:52
Bram28Bram28
60.7k44590
answered Dec 18 '18 at 2:52
Bram28Bram28
60.7k44590
60.7k44590
add a comment |
add a comment |
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1
$begingroup$
"Unless" means "if not".
$endgroup$
– David
Dec 18 '18 at 2:22
$begingroup$
So would it be !J implies !S?
$endgroup$
– martinhynesone
Dec 18 '18 at 2:28
$begingroup$
Thank you for the help!!
$endgroup$
– martinhynesone
Dec 18 '18 at 2:30
$begingroup$
@martinhynesone sorry, I had that wrong ... it ahould be $neg S rightarrow neg J$
$endgroup$
– Bram28
Dec 18 '18 at 2:31