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Validity of Arguments

These are the 3 questions I need help with. I do not understand this.

Please show all work in detail so that I understand this thing as this will help me in understanding the concepts.

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1. Determine whether the arguments are valid by means of Venn diagrams. Ensure the
Arguments are in standard form, and where necessary transform those using conversion, obversion, or contraposition operations.

Each answer must include a Venn diagram, and the validity of the argument.

a. All ears of corn with white tassels are unripe, but some ears are ripe even though their kernels are not full-sized. Therefore, some ears with full-sized kernels are not ears with white tassels.

b. Prescription drugs should never be taken without a doctor's order. So no over-
the counter drugs are prescriptive drugs, because all over-the-counter drugs can be taken without a doctor's order.

c. No one who is a Nobel Prize winner is a rock star. A number of astrophysicists are Nobel Prize winners. Therefore, a number of astrophysicists are not rock stars.

d. Only social scientists are political scientists. Many political scientists are person Who favour campaign finance reform . According, many persons who favour campaign finance reform are social scientists.

e. Not every lie is immoral, for no harmless acts are immoral and some lies are harmless.

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2. Answer the questions based on the following passage. Workings for parts (a), (b), and (c) must be shown and the rules used in the answer to part (c) must be indicated clearly.

The number of business majors increased markedly during the past decade; and if you see that happening, you know that younger people have developed a greater interest in money . Such an interest, unfortunately, means that greed has become a significant motivating force in our society; and if greed has become such a force, charity will have become insignificant. We can predict that charity will not be seen as a significant feature of this past decade.

a. Write the truth functional form of the argument above using appropriate symbols for the claims in the passage.

b. Use the truth-table method (NOT the short truth-table method) to determine if the argument is valid.

c. Using the method of deduction, determine the argument's validity.

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3. Answer the questions based on the following passage. Workings for parts (a), (b), and (c) must be shown and the rules used in the answer to part (c) must be indicated clearly.

Holmes cannot catch the train unless he gets to Charing Cross Station by noon; and if he misses the train, Watson will be in danger. Because Moriarty has thugs watching the station, Holmes can get there by noon only if he is in disguise. So, unless Holmes goes in disguise, Watson will be in danger.

a. Write the truth functional form of the argument above using appropriate symbols for the claims in the passage.

b. Use the short truth-table method to determine if the argument is valid.

c. Using the method of deduction, determine the argument's validity.

Solution Preview

First, definitions:

An argument is valid if
when the premises of the argument are true, the conclusion is also true.

You put an argument in standard form by
identifying the conclusion and listing it at the bottom, under a line, and
listing all of the statements given in support of the conclusion above the line.

1. Determine whether the arguments are valid by means of Venn diagrams. Ensure the arguments are in standard form, and where necessary transform those using conversion, obversion, or contraposition operations. Each answer must include a Venn diagram, and the validity of the argument.

a. All ears of corn with white tassels are unripe, but some ears are ripe even though their kernels are not full-sized. Therefore, some ears with full-sized kernels are not ears with white tassels.

Put this in standard form:

All ears of corn with white tassels are unripe
Some ears are ripe without full-sized kernels
Some ears with full-sized kernels are not ears with white tassels

This is not valid because you can imagine a situation in which the first two statements were true, but the conclusion was false. The statements as given are open to interpretation. Here is a possible Venn diagram for the premises:

Unripe ears Ripe ears

White tassels

Full-sized kernels

In this case, there are some ears with full-sized kernels that are not ears with white tassels. However, it would be equally true to put the green circle completely within the black circle. In that case, the first two statements would be correct, but the conclusion would not be correct. Therefore, the statement is not valid.

The fact that "some" ears are ripe without full-sized kernels does not mean that others are ripe with full sized kernels.
b. Prescription drugs should never be taken without a doctor's order. So no over-the counter-drugs are prescriptive drugs, because all over-the-counter drugs can be taken without a doctor's order.

If a drug is a prescription drug, then it was given with a doctor's order.
All OTC drugs were given without a doctor's order.
No OTC drugs are prescription drugs.

Drugs w/ doctor's order Drug's w/o doctor's order

Prescriptions OTC

This argument is valid. It is impossible to think of a scenario in which the premises of the argument are true, but the conclusion is false (this would be the case in which there is an OTC drug that is also a prescription drug).

c. No one who is a Nobel Prize winner is a rock star. A number of astrophysicists are Nobel Prize winners. Therefore, a number of astrophysicists are not rock stars.

If someone is a Nobel Prize ...

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