Chapter 6, Level 1 Self Quiz: GII

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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

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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

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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.

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.

Valid

Invalid

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