Deductive and Inductive Arguments

Make a valid hypothetical syllogism that proves "New Hampshire is north of Australia."
If Australia is to the south of New Hampshire, New Hampshire is to the north.
South of New Hampshire is Australia.
As a result, New Hampshire is located to the north of Australia.
Is your case for number one above sound? Explain why you think that is or why you don't think that is.
Since the assumption and inference are true, the statement appears to be sound; New Hampshire is in the north of Australia, and Australia is in the south of New Hampshire.
Make two examples of each of the arguments below:
Asserting the logical conclusion
1st example
If Bill Gates owns Fort Knox, he is a wealthy man.
Bill Gates is a very rich man.
So i. he possesses Fort Knox
Example 2
i. If one has the flu, then he or she has a sore throat
ii. One has a sore throat
iii. Thus, she or he has the flu.
a) Denying the antecedent
Example 1:
If I give a man a gun, the man may murder a person. If the man does not have a gun, he will then not murder a person.
Example 2:
If I work hard, I will obtain an excellent job. If I do not work hard, I will not obtain an excellent job.
b) Modus ponens
Example 1:
If a person repents, he or she will reach heaven. He or she has repented. Hence, he or she will reach heaven.
Example 2:
If you purchase today, I will offer you a twenty percent discount. You have accepted to purchase today. Thus, I will offer you a twenty percent discount.
1. Are the arguments in 3a, b, and c above valid? Sound? Explain your answers.
In 3(a), the arguments presented are invalid; for instance, despite the fact that Bill Gates is wealthy, this does not mean that he necessarily owns Fort Knox. Moreover, in spite of the fact, someone has a sore throat, this is not to say that he must have the flu.
In 3(b), the arguments presented are not logically valid. For instance, in example one, it is not true that if I do not give the man a gun, he will not kill a man; he can obtain a gun from anywhere else or use another means to kill someone. In example two, it is not a guarantee that if I work hard, I will obtain an excellent job.
In 3(c), the arguments are valid since it is evident that this is a logically dependable reasoning pattern. Fundamentally, arguments of such patterns ought to be treated as deductive at all times (Bassham, Irwin, Nardone and Wallace 59).
2. Construct a sound chain argument with the following conclusion: "If you're in Ohio, you're in North America."
If one is in Ohio, then he or she is in the United States
If one is in the U.S, then he or she is in North America
Therefore, if one is in Ohio, she or he is in North America
6. Consider the following argument:
"Oliver Wendell Holmes was an American citizen. This follows from the fact that he was a US senator, as well as from the fact that all US senators are American citizens."
a) Is it valid? Explain your answer.
The argument presented in the statement above is indeed valid since the truth seen in the premise assures logically the truth found in conclusion ("Arguments and Inference”). In this regard, only the American citizens can become the U.S. senators.
b) Is it sound? Explain. How, specifically, can you tell whether the argument is sound or unsound?
Notably, the argument presented is indeed sound since it is not just valid but starts with a premise, which is true. For instance, it is a truth Wendell Holmes was a U.S. Citizen, and this can be proved by the fact that he became the US senator; and to hold this political office, one has to be a US citizen (“Qualifications Needed”).
7. Construct a strong argument for this conclusion:
“Most of the northern U.S. states vote for the Republican Presidential candidate.”
The Republicans dominate the northern states.
Therefore, most of the states in the north vote for the Republican Presidential candidate.
8. Explain why your argument is strong. Is your argument cogent? Explain.
The argument is a strong one since it has true premises and perhaps a real conclusion.

Work Cited
"Arguments and Inference." Philosophy Pages, 2017. http://www.philosophypages.com/lg/e01.htm. Accessed 22 Jul. 2017.
Bassham, Gregory, Irwin William, Nardone Henry, and Wallace James M. Critical Thinking: A Student’s Introduction. 4 or 5th Ed. McGraw Hill, 2010.
“Qualifications Needed to Become a U.S. Senator.” Study.com, 2017. http://study.com/articles/Qualifications_Needed_to_Become_a_US_Senator.html. Accessed 22 Jul. 2017.