Introductory Logic
Test #1
January 6, 2006
Name: ________________________
R. Hammack
Score: _________

1. (20 points) Identify each of the following passages as an argument or a non-argument. If the passage is an argument, underline the conclusion.

Implied and express claims of product safety refer to the degree of risk associated with using a product. Since the use of virtually any product involves some degree of risk, questions of safety are essentially questions of acceptable known levels of risk.
(M. Velasquez, "The ethiscs of consumer Production")

Not everything oxygen does is desirable. It causes iron to rust and copper to corode. It causes food to spoil and it aids in the decay of wood.
(J.Hill and D. Kolb, Chemestry for Changing Times)

The period of 1648—1789 was one of competition among the primary monarchs of Europe. Wars among the great powers were frequent but limited. France made major efforts to become paramount, but the balance of power operated to block French expansion.
(S. Spiegel, World Politics in a New Era)

A chess problem is mathematics, but it is in some way `trivial' mathematics
(G. Hardy, A Mathematicians's Apology)

If conditions worsen further so that a massive nuclear first strike can only be deterred by the bluff or threat of a massive nuclear retaliation, then it would be morally justified to bluff but not threaten massive nuclear retaliation.
(J. Sterba, "Just War Theory on Nuclear Strategy")

2. (30 points) Each of the following passages is an argument. Underline the conclusion. Say if the argument is deductive, inductive, valid, invalid, weak, strong, and (if possible) sound, unsound, cogent, or uncogent.

All spiders have wings, because all spiders are birds, and all birds have wings.

Some Americans are blonde. Some Americans are women. Therefore it follows with absolute certainty that some Americans are blonde women.

Almost exactly half of the people in the U.S. are women. Thus, very close to half of the people in Virginia are women.

If you do not attend a class, then you will fail it. If you fail a class, then you will not get credit for it. Therefore, if you do not attend a class, then you will not get credit for it.

Since lots of people have won over $1000 in the Virginia lottery, I will probably win that much if I play the lottery today.

Since most students at Randolph-Macon are billionaires, it's very likely that there are a few billionaires in our Logic class.

. (14 points) Use the counterexample method to prove each of the following arguments is invalid.

All corporations that overcharge their customers are unethical businesses.
Some unethical businesses are investor-owned utilities.
Thus, some investor-owned utilities are corporations that overcharge their customers.

Argument Form:

All C are U.
Some U are I.
Thus some I are C
Subsititution Instance:

C = cats
U = animals
I = dogs
Resulting Argument:

All cats are animals. (T)
Some animals are dogs. (T)
Thus some dogs are cats. (F)

Since the argument can be transformed into one with true premises and false conclusion, it is INVALID.

If the government imposes import restrictions, then the price of automobiles will rise. Therefore, the price of automobiles will not rise, since the government will not impose import restrictions.

Argument Form:

If G then P.
It is not true that G.
Thus it is not true that P.
Substitution Instance

G = "George Washington was hanged"
P = "George Washington is dead"
Resulting Argument:

If George Washington was hanged, then George Washington is dead. (T)
It is not true that George Washington was hanged. (T)
Therefore it is not true that George Washington is dead (F)

Since the argument can be transformed into one with true premises and false conclusion, it is INVALID.

4. (8 points) Diagram the following extended argument.

  (1) Research leading to the development of the scramjet engine is worthwhile. (2) Commercial aircraft incorporating such an engine could cross the Pacific in as little as two hours. (3) This would relieve the fatigue of flights from New York to Tokyo. Also, (4) such an engine could power future orbiting spacecraft.
(T. Heppenheimer, "A Plane for Space")

                     (3)     (4)
                       \     /
                        \   /
                         \ /

5. (14 points) Decide if the following immediate inferences are valid or invalid. Use either Venn diagrams or the Modern Square of Opposition.

No vampires are avid consumers of garlic bread.
Therefore, it is false that some vampires are avid consumers of garlic bread.

The diagram for the premise is:

The conclusion says it's false that:
which means there's nothing in the middle, so the conclusion says
Since the premise and conclusion are expressing the same thing, the argument is VALID.

Some country doctors are altruistic healers.
Therefore, some country doctors are not altruistic healers.

  The Venn diagrams for the premise and the conclusion are drawn. Notice these diagrams express different things, so the premise is saying something the conclusion isn't.

Thus the argument is invalid.

6. (14 points) Use Venn Diagrams to decide if the following arguments are valid or invalid.

No A are B.
Some C are not B.
Therefore, some C are A.


Here is the Venn diagram for the argument.
Notice that the premises do not contain enough information
to tell us whether the X is inside A or outside A.

For the couclusion to be true, the X would have to be outside A.
Since this can't be deduced from the premises, the
argument is INVALID.

All compounds that destroy the ozone layer are environmental hazards.
All chlorofluorocarbons are compounds that destroy the ozone layer.
Thus, all chlorofluorocarbons are environmental hazards.


The argument form is

All C are H.
All F are C.
Thus all F are H.

Here is the Venn diagram for the argument.
Notice that the premises do imply the conclusion.

Thus the argument is VALID.