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Is the argument below valid?
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If interest rates go down, then I will buy a house. If I buy a house, I will need
a loan. Therefore, I will not need a loan if I do not buy a house.
Is this argument valid?
logic
edited yesterday
Frank Hubeny
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asked yesterday
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
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show 1 more comment
If interest rates go down, then I will buy a house. If I buy a house, I will need
a loan. Therefore, I will not need a loan if I do not buy a house.
Is this argument valid?
logic
edited yesterday
Frank Hubeny
10.5k51558
asked yesterday
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
111
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
11 hours ago
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
11 hours ago
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
11 hours ago
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
11 hours ago
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
9 hours ago
|
show 1 more comment
If interest rates go down, then I will buy a house. If I buy a house, I will need
a loan. Therefore, I will not need a loan if I do not buy a house.
Is this argument valid?
logic
edited yesterday
Frank Hubeny
10.5k51558
asked yesterday
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
111
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
If interest rates go down, then I will buy a house. If I buy a house, I will need
a loan. Therefore, I will not need a loan if I do not buy a house.
Is this argument valid?
logic
logic
edited yesterday
Frank Hubeny
10.5k51558
asked yesterday
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
111
New contributor
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Check out our Code of Conduct.
edited yesterday
Frank Hubeny
10.5k51558
asked yesterday
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
111
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edited yesterday
Frank Hubeny
10.5k51558
edited yesterday
Frank Hubeny
10.5k51558
edited yesterday
Frank Hubeny
10.5k51558
10.5k51558
asked yesterday
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
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asked yesterday
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
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asked yesterday
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
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111
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Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
11 hours ago
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
11 hours ago
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
11 hours ago
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
11 hours ago
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
9 hours ago
|
show 1 more comment
Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
11 hours ago
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
11 hours ago
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
11 hours ago
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
11 hours ago
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
9 hours ago
Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
11 hours ago
Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
11 hours ago
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
11 hours ago
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
11 hours ago
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
11 hours ago
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
11 hours ago
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
11 hours ago
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
11 hours ago
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
9 hours ago
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
9 hours ago
|
show 1 more comment
4 Answers
4
active
oldest
votes
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered yesterday
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
add a comment |
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered yesterday
Frank HubenyFrank Hubeny
10.5k51558
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
11 hours ago
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
11 hours ago
add a comment |
The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered 19 hours ago
YoupTYoupT
636
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All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered 12 hours ago
jeancallistijeancallisti
312
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered yesterday
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
add a comment |
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered yesterday
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
add a comment |
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered yesterday
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered yesterday
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
answered yesterday
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
answered yesterday
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
answered yesterday
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
29.8k22065
add a comment |
add a comment |
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered yesterday
Frank HubenyFrank Hubeny
10.5k51558
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
11 hours ago
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
11 hours ago
add a comment |
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered yesterday
Frank HubenyFrank Hubeny
10.5k51558
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
11 hours ago
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
11 hours ago
add a comment |
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered yesterday
Frank HubenyFrank Hubeny
10.5k51558
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered yesterday
Frank HubenyFrank Hubeny
10.5k51558
answered yesterday
Frank HubenyFrank Hubeny
10.5k51558
answered yesterday
Frank HubenyFrank Hubeny
10.5k51558
answered yesterday
Frank HubenyFrank Hubeny
10.5k51558
10.5k51558
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
11 hours ago
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
11 hours ago
add a comment |
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
11 hours ago
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
11 hours ago
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
11 hours ago
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
11 hours ago
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
11 hours ago
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
11 hours ago
add a comment |
The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered 19 hours ago
YoupTYoupT
636
New contributor
YoupT is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered 19 hours ago
YoupTYoupT
636
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YoupT is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered 19 hours ago
YoupTYoupT
636
New contributor
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The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered 19 hours ago
YoupTYoupT
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answered 19 hours ago
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answered 19 hours ago
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answered 19 hours ago
YoupTYoupT
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All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered 12 hours ago
jeancallistijeancallisti
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All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered 12 hours ago
jeancallistijeancallisti
312
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jeancallisti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered 12 hours ago
jeancallistijeancallisti
312
New contributor
jeancallisti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered 12 hours ago
jeancallistijeancallisti
312
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edited 12 hours ago
answered 12 hours ago
jeancallistijeancallisti
312
New contributor
jeancallisti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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answered 12 hours ago
jeancallistijeancallisti
312
answered 12 hours ago
jeancallistijeancallisti
312
312
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jeancallisti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
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jeancallisti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
add a comment |
Bruce Grayton Toodeep Muzawazi is a new contributor. Be nice, and check out our Code of Conduct.
Bruce Grayton Toodeep Muzawazi is a new contributor. Be nice, and check out our Code of Conduct.
Bruce Grayton Toodeep Muzawazi is a new contributor. Be nice, and check out our Code of Conduct.
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Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
11 hours ago
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
11 hours ago
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
11 hours ago
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
11 hours ago
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
9 hours ago