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Return to Logic 5e Student Resources
6G Practice: Ordinary Language Arguments - Standard-form translations, and determining whether arguments are valid or invalid
Quiz Content
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not completed
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The following syllogism needs to be rewritten into standard form. Use the tools discussed in this section to reduce the number of terms. Then use Venn diagrams and the six rules to determine whether the syllogism is valid or invalid under the modern interpretation. You may pick only one answer choice.
Some A are non-B.
All B are non-C.
Some C are not A.
Valid
correct
incorrect
Invalid: Rule 1 is broken.
correct
incorrect
Invalid: Rule 2 is broken.
correct
incorrect
Invalid: Rule 5 is broken.
correct
incorrect
b, c, and d are correct.
correct
incorrect
*
not completed
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The following syllogism needs to be rewritten into standard form. Use the tools discussed in this section to reduce the number of terms. Then use Venn diagrams and the six rules to determine whether the syllogism is valid or invalid under the modern interpretation. You may pick only one answer choice.
All non-A are non-C.
Some A are non-B.
All C are B.
Valid
correct
incorrect
Invalid: Rule 1 is broken.
correct
incorrect
Invalid: Rule 2 is broken.
correct
incorrect
Invalid: Rule 3 is broken.
correct
incorrect
Invalid: Rule 4 is broken.
correct
incorrect
*
not completed
.
The following syllogism needs to be rewritten into standard form. Use the tools discussed in this section to reduce the number of terms. Then use Venn diagrams and the six rules to determine whether the syllogism is valid or invalid under the modern interpretation. You may pick only one answer choice.
All C are A.
All A are B.
All non-C are non-B.
Valid
correct
incorrect
Invalid: Rule 1 is broken.
correct
incorrect
Invalid: Rule 2 is broken.
correct
incorrect
Invalid: Rule 3 is broken.
correct
incorrect
Invalid: Rule 4 is broken.
correct
incorrect
*
not completed
.
The following argument needs to be translated into standard form. Use all the tools discussed so farâ€”including reducing the number of terms, and paraphrasing.
Refurbished computers are not expensive, because every computer my uncle buys is refurbished, and every computer he buys is inexpensive.
Let R =
refurbished computers
, E =
expensive things
, and U =
computers bought by my uncle
All E are non-U. All U are non-E.
All U are R.
Rewritten as:
All U are R.
No R are E. All non-E are R.
correct
incorrect
All non-E are U. All U are non-E.
All U are R.
Rewritten as:
All R are U.
No R are E. All R are non-E.
correct
incorrect
All U are non-E. All U are non-E.
All U are R.
Rewritten as:
All U are R.
No R are E. All R are non-E.
correct
incorrect
All U are non-E. All non-E are U.
All U are R.
Rewritten as:
All U are R.
No non-E are R. All R are non-E.
correct
incorrect
*
not completed
.
Use a Venn diagram and the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
Refurbished computers are not expensive, because every computer my uncle buys is refurbished, and every computer he buys is inexpensive.
Let R =
refurbished computers
, E =
expensive things
, and U =
computers bought by my uncle
Valid
correct
incorrect
Invalid
correct
incorrect
*
not completed
.
The following argument needs to be translated into standard form. Use all the tools discussed so farâ€”including reducing the number of terms, and paraphrasing.
Some starvation diets are effective ways to lose weight. However, starving yourself is bad for your heart. Thus, some effective ways to lose weight are bad for your heart.
Let S =
starvation diets
, E =
effective ways to lose weight
, and B =
things that are bad for your heart
Some S are B.
All S are E.
Some E are B.
correct
incorrect
Some E are A.
All S are B.
Some E are B.
correct
incorrect
Some S are E.
All B are S.
Some E are B.
correct
incorrect
Some E are S.
All S are B.
Some B are E.
correct
incorrect
*
not completed
.
Use a Venn diagram and the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
Some starvation diets are effective ways to lose weight. However, starving yourself is bad for your heart. Thus, some effective ways to lose weight are bad for your heart.
Let S =
starvation diets
, E =
effective ways to lose weight
, and B =
things that are bad for your heart
Valid
correct
incorrect
Invalid
correct
incorrect
*
not completed
.
The following argument needs to be translated into standard form. Use all the tools discussed so farâ€”including reducing the number of terms, and paraphrasing.
Traditional Western philosophy is a series of footnotes to Plato. However, since Asian philosophy is not part of traditional Western philosophy, we can conclude that Asian philosophy is not a series of footnotes to Plato.
Let T =
Traditional Western philosophy
, F =
a series of footnotes to Plato
, and A =
Asian philosophy is not part of traditional Western philosophy
All T are F.
No A are T.
No A are F.
correct
incorrect
All T are F.
No T are A.
No F are A.
correct
incorrect
All F are T.
No A are T.
No A are F.
correct
incorrect
All T are F.
No T are A.
No F are A.
correct
incorrect
*
not completed
.
Use a Venn diagram and the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
Traditional Western philosophy is a series of footnotes to Plato. However, since Asian philosophy is not part of traditional Western philosophy, we can conclude that Asian philosophy is not a series of footnotes to Plato.
Let T =
Traditional Western philosophy
, F =
a series of footnotes to Plato
, and A =
Asian philosophy is not part of traditional Western philosophy
Valid
correct
incorrect
Invalid
correct
incorrect
*
not completed
.
The following argument needs to be translated and rewritten into standard form. Use the tools discussed in this section to reduce the number of terms.
All self-motivated students are using their intellectual capabilities. But no disinterested students are using their intellectual capabilities. Therefore, all self-motivated students are interested students.
Let S =
self-motivated students
, I =
students using their intellectual capabilities
, D =
disinterested students
, non-D =
interested students
.
All I are S. All S are I.
No D are I.
Rewritten as:
No D are I.
All S are non-D. No S are D.
correct
incorrect
All S are I. All S are I.
No D are I.
Rewritten as:
No D are I.
All S are non-D. No S are D.
correct
incorrect
All S are I. All S are I.
No I are D.
Rewritten as:
No D are I.
All S are non-D. No non-S are D.
correct
incorrect
All S are I. All S are I.
No D are I.
Rewritten as:
No D are I.
All S are non-D. No S are D.
correct
incorrect
*
not completed
.
Use a Venn diagram and the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
All self-motivated students are using their intellectual capabilities. But no disinterested students are using their intellectual capabilities. Therefore, all self-motivated students are interested students.
Let S =
self-motivated students
, I =
students using their intellectual capabilities
, D =
disinterested students
, non-D =
interested students
.
Valid
correct
incorrect
Invalid
correct
incorrect
*
not completed
.
The following argument needs to be translated and rewritten into standard form. Use the tools discussed in this section to reduce the number of terms.
Some preschool children are severely overweight. Some obese students are susceptible to diabetes. Therefore, some preschool children are not susceptible to diabetes.
Let P =
pre-school children
, S =
severely overweight students
, O =
obese students
, and D =
people susceptible to diabetes
Some P are S. Some P are S.
Some O are D.
Rewritten as:
Some S are D.
Some P are not D. Some P are not D.
correct
incorrect
Some S are P. Some P are S.
Some O are D.
Rewritten as:
Some S are D.
Some P are D. Some P are not D.
correct
incorrect
Some P are S. Some P are S.
Some O are D.
Rewritten as:
Some S are D.
Some P are D. Some P are not D.
correct
incorrect
Some P are S. Some P are S.
Some O are not D.
Rewritten as:
Some S are D.
Some P are not D. Some P are D.
correct
incorrect
*
not completed
.
Use a Venn diagram and the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
Some preschool children are severely overweight. Some obese students are susceptible to diabetes. Therefore, some preschool children are not susceptible to diabetes.
Let P =
pre-school children
, S =
severely overweight students
, O =
obese students
, and D =
people susceptible to diabetes
Valid
correct
incorrect
Invalid
correct
incorrect
*
not completed
.
Use the tools discussed in this section to reduce the number of terms in the following syllogism. Then use the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
All C are B.
All B are A.
All A are non-C.
Valid
correct
incorrect
Invalid: Rule 1 is broken.
correct
incorrect
Invalid: Rule 2 is broken.
correct
incorrect
Invalid: Rule 4 is broken.
correct
incorrect
Invalid: Rule 5 is broken.
correct
incorrect
*
not completed
.
Use the tools discussed in this section to reduce the number of terms in the following syllogism. Then use the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
All B are A.
Some B are non-C.
Some C are not A.
Valid
correct
incorrect
Invalid: Rule 2 and Rule 3 are broken.
correct
incorrect
Invalid: Rule 2 and Rule 4 are broken.
correct
incorrect
Invalid: Rule 2 and Rule 5 are broken.
correct
incorrect
Invalid: Rule 2 and Rule 6 are broken.
correct
incorrect
*
not completed
.
Use the tools discussed in this section to reduce the number of terms in the following syllogism. Then use the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
No B are non-A.
All A are non-C.
No C are B.
Valid
correct
incorrect
Invalid: Rule 2 is broken.
correct
incorrect
Invalid: Rule 3 is broken.
correct
incorrect
Invalid: Rule 5 is broken.
correct
incorrect
Invalid: Rule 6 is broken.
correct
incorrect
*
not completed
.
Use the tools discussed in this section to reduce the number of terms in the following syllogism. Then use the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
All C are B.
No A are C.
Some C are not non-B.
Valid
correct
incorrect
Invalid: Rule 1 is broken.
correct
incorrect
Invalid: Rule 2 is broken.
correct
incorrect
Invalid: Rule 3 is broken.
correct
incorrect
Invalid: Rule 4 is broken.
correct
incorrect
*
not completed
.
Use the tools discussed in this section to reduce the number of terms in the following syllogism. Then use the six rules to determine whether the syllogism is valid or invalid under the modern interpretation.
No C are B.
Some A are B.
Some C are A.
Valid
correct
incorrect
Invalid: Rule 1, Rule, 2, and Rule 3 are broken.
correct
incorrect
Invalid: Rule 2, Rule 3, and Rule 4 are broken.
correct
incorrect
Invalid: Rule 3, Rule 4, and Rule 5 are broken.
correct
incorrect
Invalid: Rule 4, Rule 5, and Rule 6 are broken.
correct
incorrect
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