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 9 hours ago
Frank Hubeny
10.5k51558
asked 9 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
61
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.
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 9 hours ago
Frank Hubeny
10.5k51558
asked 9 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
61
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
9 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 9 hours ago
Frank Hubeny
10.5k51558
asked 9 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
61
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 9 hours ago
Frank Hubeny
10.5k51558
asked 9 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
61
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 9 hours ago
Frank Hubeny
10.5k51558
asked 9 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
61
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 9 hours ago
Frank Hubeny
10.5k51558
edited 9 hours ago
Frank Hubeny
10.5k51558
edited 9 hours ago
Frank Hubeny
10.5k51558
10.5k51558
asked 9 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
61
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.
asked 9 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
61
asked 9 hours ago
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
61
61
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.
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.
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
9 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
9 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
9 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
9 hours ago
add a comment |
2 Answers
2
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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 9 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 9 hours ago
Frank HubenyFrank Hubeny
10.5k51558
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
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active
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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 9 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 9 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 9 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 9 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
answered 9 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
answered 9 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.7k22065
answered 9 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 9 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 9 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 9 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 9 hours ago
Frank HubenyFrank Hubeny
10.5k51558
answered 9 hours ago
Frank HubenyFrank Hubeny
10.5k51558
answered 9 hours ago
Frank HubenyFrank Hubeny
10.5k51558
answered 9 hours ago
Frank HubenyFrank Hubeny
10.5k51558
10.5k51558
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
9 hours ago