6G Practice: Ordinary Language Arguments - Standard-form translations, and determining whether arguments are valid or invalid - Logic 5e Student Resources

. 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

Invalid: Rule 1 is broken.

Invalid: Rule 2 is broken.

Invalid: Rule 5 is broken.

b, c, and d are correct.

. 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

Invalid: Rule 1 is broken.

Invalid: Rule 2 is broken.

Invalid: Rule 3 is broken.

Invalid: Rule 4 is broken.

. 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

Invalid: Rule 1 is broken.

Invalid: Rule 2 is broken.

Invalid: Rule 3 is broken.

Invalid: Rule 4 is broken.

. The following argument needs to be translated into standard form. Use all the tools discussed so far—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.

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.

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.

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.

. 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

Invalid

. The following argument needs to be translated into standard form. Use all the tools discussed so far—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.

Some E are A.
All S are B.
Some E are B.

Some S are E.
All B are S.
Some E are B.

Some E are S.
All S are B.
Some B are E.

. 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

Invalid

. The following argument needs to be translated into standard form. Use all the tools discussed so far—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.

All T are F.
No T are A.
No F are A.

All F are T.
No A are T.
No A are F.

All T are F.
No T are A.
No F are A.

. 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

Invalid

. 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.

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.

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.

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.

. 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

Invalid

. 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.

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.

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.

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.

. 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

Invalid

. 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

Invalid: Rule 1 is broken.

Invalid: Rule 2 is broken.

Invalid: Rule 4 is broken.

Invalid: Rule 5 is broken.

. 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

Invalid: Rule 2 and Rule 3 are broken.

Invalid: Rule 2 and Rule 4 are broken.

Invalid: Rule 2 and Rule 5 are broken.

Invalid: Rule 2 and Rule 6 are broken.

. 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

Invalid: Rule 2 is broken.

Invalid: Rule 3 is broken.

Invalid: Rule 5 is broken.

Invalid: Rule 6 is broken.

. 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

Invalid: Rule 1 is broken.

Invalid: Rule 2 is broken.

Invalid: Rule 3 is broken.

Invalid: Rule 4 is broken.

. 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

Invalid: Rule 1, Rule, 2, and Rule 3 are broken.

Invalid: Rule 2, Rule 3, and Rule 4 are broken.

Invalid: Rule 3, Rule 4, and Rule 5 are broken.

Invalid: Rule 4, Rule 5, and Rule 6 are broken.