I.
Define:
1. Valid Argument:
An argument such that if the premises are true, then the conclusion must be true.
2. Invalid Argument:
An argument where it is possible to have all true premises and a false conclusion.
II.
Assume the premises of the following arguments are true.
Determine if:
a) The argument is invalid or valid (write valid, or invalid)
b) If the argument is invalid, add an additional premise(s) which will make the
conclusion false while not changing the truth of the existing premises. 3. If the price of gas continues to increase, the price of consumer goods which require vehicular transportation will increase also. The price of gas did not increase, therefore the prices of consumer goods requiring vehicular transportation did not increase. The argument is invalid. An additional premise which would not change the truth of the stated premises, but would make the premise false is, “ An increase in wages for truck drivers also increases the price of consumer goods requiring vehicular transportation, and all truck drivers received a wag increase” 4. Either the battery is low on the car, or the alternator is bad. The alternator is not bad. Therefore the battery is low. The argument is valid. 5. If you take Claritin, your allergies will be better Your allergies are better. Therefore you took Claritin. The argument is invalid. Add the additional premise, “Allergies improve when there are fewer allergens in the air, and there were fewer allergens the day your allergies were better” 6. If gravity is reducible to a geometric expression of Space-time, then light waves will always follow the straightest path provided by that geometry. Light waves do not always follow the straightest path provided by that geometry Therefore gravity is not reducible to a geometric expression of space-time. The argument is valid. (Because it has the form” If P then Q Not Q Therefore Not P) 7. If autistic children are the real authors of the text in question, then it will make no difference if the children see something different than their facilitators. It does make a difference when the children see something different than their facilitators. Therefore, the autistic children are not the real authors of the text in question. The argument is valid. (It has the same form as 6 above) 8. If John buys a house, then he will move from his current residence. If he moves from his current residence, we will have to help him move his furniture. Therefore if John buys a house, then we will have to help them move his furniture. The argument is valid. (It has the form: If P then Q If Q then S Therefore If P then S)
III.
Circle any statements which are entailed by following sentences.
11. John is a bachelor and works the night shift.
a) John's wife works the day shift.
b) John is male
c) John makes night-shift wages.
d) John is not married.
12. Today is not Monday.
a) Today is Tuesday.
b) Tomorrow is not Tuesday.
c) Tomorrow is Monday.
d) Yesterday was not Monday.

13. Kevin knows all the Capitols of the United States of America.

a) Kevin knows the Capitol of Puerto Rico b) Kevin does not know the capitol of Virginia. c) Kevin knows the capitol of Kentucky and Maine d) Kevin knows the capitol of Mexico.
IV.
Below are several arguments. Assume all premises are true.
a) Determine whether the argument is valid or invalid:
b) If the argument is Invalid, state whether it is an instance of strong induction, an
argument by analogy, or a logical fallacy. c) Finally, based on the above considerations, state whether you think the argument strongly supports the conclusion, or weakly supports the conclusion. Give reasons for determining your judgment of the strength, weakness, soundness or fallaciousness of the argument’s conclusion. d) Note – If you determine that the argument is Valid, then simply write VALID (since on the assumption of true premises, the conclusion must be true) The radio runs on either battery power or a/c. If it is running on a/c, then it will be plugged in. It is not plugged in. Therefore it is running on battery power. Valid If it pours rain in a flash-flood, then the washes will fill with water and become impossible to cross. The washes are impossible to cross. Therefore it poured rain in a flash-flood. Invalid – The particular name of this fallacy is “Affirming the consequent” – if one adds the additional premises “Washes also can become impossible to cross if a dam breaks, and dam did indeed break” the conclusion becomes false. The strength of the argument depends on where the wash is located and if there are other factors which normally occur besides rainfall which cause the washes to be impossible to cross. Maria Santa Elena knows the future by consulting her tarot cards. She once said that someone would attempt to kill an American president, and then Lee Harvey Oswald shot president Kennedy. She also foresaw the 9-11 attacks by predicting “Great disasters will befall Americans”. Of course she has predicted things which have not happened, but that does not mean she is wrong, only that they have not yet happened. This argument is invalid. It commits the fallacy “argument from ignorance” in that the conclusion is not capable of being shown false. The argument is also ambiguous in nature, since many things can be counted as “great disasters” As stated the argument is weak. We must reject the current legal movement toward the legitimization of gay marriages, since it is obviously part of a liberal agenda! This is a fallacy. The conclusion proceeds from one premise only. The connection between gay marriages and liberal agenda is not spelled out, nor are any reasons given for rejection of such marriages. It commits the fallacy of complex question or/and bandwagon or false association. As stated the argument is weak. My friend Nancy works in a hospital where people are admitted for drug abuse problems. Many of her patients have problems with alcohol, other with meta-amphetamines, others with valium others with crack-cocaine, others with pain killers. All of these patients that Nancy works with have lost their jobs, been alienated from their family members, and have suffered serious health consequences due to their drug addiction. Therefore, the punishment for drug use should be increased to insure no one goes down this terrible destructive path. This argument is invalid. Nancy’s position in the hospital almost ensures her that she will only see patients who have problems – thus there is a natural filtering – bias effect in Nancy’s experience. There is also no connection stated between punishment and drug use, which needs to be established before such conclusion is accepted. As stated, there are few reasons for believing the conclusion, therefore it is a weak argument. Define the following terms:
5. Validity- An argument whose conclusion must be true if no premises are false.
6. Consistency – A set of proposition which may all be true – which means there are
no contraries or contradictions among the propositions.

7. Contradiction- A unique proposition related to another proposition such that if one
proposition is true, the other must be false, and visa-versa. One of the pair MUST be
true. A contradiction is the simple NEGATION of one statement.

8. Contrary Statement – any number of statements related to an original statement
and each other, such that if any one is true, all the others must be false, however, all
of the statements may be false.

9. Soundness – A valid argument with all true premises,
10. Entailment – A relationship between two statements P and Q, where it is said that
P entails Q, if and only if it is impossible for Q to be false when P is true.
e.g. John is a bachelor entails that John is not married.

16. Write the contradiction to the following propositions:

a) No atoms are larger than 1 micron.
At least one atom is larger than 1 micron.

b) The earth is covered mostly by water.
The earth is not covered mostly by water.

c) Insects are animals.
Insects are not animals.

d) At least 10 people die each day in car accidents.
No people die each day in car accidents.
(Hint: Here the phrase, “At least 10 people” is the same as saying, “Some people”)
7. Write 3 contraries for each of the following propositions.

a) Today is November 11, 2002.

Today is November 10, 2002

Today is November 9, 2002
Today is November 8, 2002

b) Al Gore lost the election by less than 20,000 votes.
Al Gore won the election by less than 20,000 votes.
Al Gore lost the election by 20,000 votes exactly.
Al Gore lost the election by more than 20,000 votes.

c) Logic is only the study of symbols and rules for their manipulation.
Logic is only the study of symbols.
Logic is only the study of rules.
Logic is the study of symbols and rules for their manipulation and the assumptions