Is the argument below valid?
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 12 hours ago
Frank Hubeny
10.5k51558
asked 12 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
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add a 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 12 hours ago
Frank Hubeny
10.5k51558
asked 12 hours ago
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.
I made an edit. You may roll this back if it does not represent your view by clicking on the "edited" link above my image and then on a rollback link. Welcome!
– Frank Hubeny
12 hours ago
add a 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 12 hours ago
Frank Hubeny
10.5k51558
asked 12 hours ago
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 12 hours ago
Frank Hubeny
10.5k51558
asked 12 hours ago
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.
edited 12 hours ago
Frank Hubeny
10.5k51558
asked 12 hours ago
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.
edited 12 hours ago
Frank Hubeny
10.5k51558
edited 12 hours ago
Frank Hubeny
10.5k51558
edited 12 hours ago
Frank Hubeny
10.5k51558
10.5k51558
asked 12 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
111
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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.
asked 12 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
111
asked 12 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
111
111
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Bruce Grayton Toodeep Muzawazi 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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Check out our Code of Conduct.
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Check out our Code of Conduct.
I made an edit. You may roll this back if it does not represent your view by clicking on the "edited" link above my image and then on a rollback link. Welcome!
– Frank Hubeny
12 hours ago
add a comment |
I made an edit. You may roll this back if it does not represent your view by clicking on the "edited" link above my image and then on a rollback link. Welcome!
– Frank Hubeny
12 hours ago
I made an edit. You may roll this back if it does not represent your view by clicking on the "edited" link above my image and then on a rollback link. Welcome!
– Frank Hubeny
12 hours ago
I made an edit. You may roll this back if it does not represent your view by clicking on the "edited" link above my image and then on a rollback link. Welcome!
– Frank Hubeny
12 hours ago
add a comment |
3 Answers
3
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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 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
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 12 hours ago
Frank HubenyFrank Hubeny
10.5k51558
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 42 mins ago
YoupTYoupT
235
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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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3 Answers
3
active
oldest
votes
3 Answers
3
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 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
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 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
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 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
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 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
answered 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
answered 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
answered 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
29.7k22065
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 12 hours ago
Frank HubenyFrank Hubeny
10.5k51558
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 12 hours ago
Frank HubenyFrank Hubeny
10.5k51558
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 12 hours ago
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 12 hours ago
Frank HubenyFrank Hubeny
10.5k51558
answered 12 hours ago
Frank HubenyFrank Hubeny
10.5k51558
answered 12 hours ago
Frank HubenyFrank Hubeny
10.5k51558
answered 12 hours ago
Frank HubenyFrank Hubeny
10.5k51558
10.5k51558
add a comment |
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 42 mins ago
YoupTYoupT
235
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 42 mins ago
YoupTYoupT
235
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 42 mins ago
YoupTYoupT
235
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.
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 42 mins ago
YoupTYoupT
235
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.
answered 42 mins ago
YoupTYoupT
235
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.
answered 42 mins ago
YoupTYoupT
235
answered 42 mins ago
YoupTYoupT
235
235
New contributor
YoupT is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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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.
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 |
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.
Bruce Grayton Toodeep Muzawazi is a new contributor. Be nice, and check out our Code of Conduct.
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I made an edit. You may roll this back if it does not represent your view by clicking on the "edited" link above my image and then on a rollback link. Welcome!
– Frank Hubeny
12 hours ago