Truth set of this predicate
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So say I have the following predicate:
$P(x): x = x + 1$
Which is in the domain of the integers ($Z$).
Is the truth set for this predicate empty or is it:
0, 1, 2, 3, 4, 5 ...
discrete-mathematics predicate-logic
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up vote
-1
down vote
favorite
So say I have the following predicate:
$P(x): x = x + 1$
Which is in the domain of the integers ($Z$).
Is the truth set for this predicate empty or is it:
0, 1, 2, 3, 4, 5 ...
discrete-mathematics predicate-logic
2
In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
â esotechnica
Aug 19 at 7:34
@esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
â Sphero
Aug 19 at 7:38
1
Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
â esotechnica
Aug 19 at 7:41
Okay, thanks for the help.
â Sphero
Aug 19 at 7:43
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
So say I have the following predicate:
$P(x): x = x + 1$
Which is in the domain of the integers ($Z$).
Is the truth set for this predicate empty or is it:
0, 1, 2, 3, 4, 5 ...
discrete-mathematics predicate-logic
So say I have the following predicate:
$P(x): x = x + 1$
Which is in the domain of the integers ($Z$).
Is the truth set for this predicate empty or is it:
0, 1, 2, 3, 4, 5 ...
discrete-mathematics predicate-logic
asked Aug 19 at 7:29
Sphero
147
147
2
In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
â esotechnica
Aug 19 at 7:34
@esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
â Sphero
Aug 19 at 7:38
1
Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
â esotechnica
Aug 19 at 7:41
Okay, thanks for the help.
â Sphero
Aug 19 at 7:43
add a comment |Â
2
In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
â esotechnica
Aug 19 at 7:34
@esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
â Sphero
Aug 19 at 7:38
1
Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
â esotechnica
Aug 19 at 7:41
Okay, thanks for the help.
â Sphero
Aug 19 at 7:43
2
2
In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
â esotechnica
Aug 19 at 7:34
In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
â esotechnica
Aug 19 at 7:34
@esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
â Sphero
Aug 19 at 7:38
@esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
â Sphero
Aug 19 at 7:38
1
1
Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
â esotechnica
Aug 19 at 7:41
Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
â esotechnica
Aug 19 at 7:41
Okay, thanks for the help.
â Sphero
Aug 19 at 7:43
Okay, thanks for the help.
â Sphero
Aug 19 at 7:43
add a comment |Â
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2
In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
â esotechnica
Aug 19 at 7:34
@esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
â Sphero
Aug 19 at 7:38
1
Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
â esotechnica
Aug 19 at 7:41
Okay, thanks for the help.
â Sphero
Aug 19 at 7:43