Indicate whether each of the following arguments is valid...

Indicate whether each of the following arguments is valid and whether it is sound. Explain your answers where necessary. 1. Most professors agree that they are paid too little, so they are. 2. David Letterman is over four feet tall, so he is over two feet tall. 3. Lee can't run a company right, because he can't do anything right. 4. Barack Obama is smart and good-looking, so he is smart. 5. Barack Obama is either a Democrat or a Republican, so he is a Democrat. 6. Since Jimmy Carter was president, he must have won an election. 7. Since Gerald Ford was president, he must have won an election. 8. Pat is either a mother or a father. If Pat is a mother, then she is a parent. If Pat is a father, he is a parent. So, either way, Pat is a parent. (Assume that this conclusion is true.) 9. People who live in the Carolinas live in either North Carolina or South Carolina. Hillary Clinton does not live in North Carolina or South Carolina. Hence, she does not live in the Carolinas. 10. If all of Illinois were in Canada, then Chicago would be in Canada. But Chicago is not in Canada. Therefore, not all of Illinois is in Canada.

Indicate whether each of the following arguments is valid and whether it is sound. Explain your answers where necessary.
1. Most professors agree that they are paid too little, so they are.
2. David Letterman is over four feet tall, so he is over two feet tall.
3. Lee can't run a company right, because he can't do anything right.
4. Barack Obama is smart and good-looking, so he is smart.
5. Barack Obama is either a Democrat or a Republican, so he is a Democrat.
6. Since Jimmy Carter was president, he must have won an election.
7. Since Gerald Ford was president, he must have won an election.
8. Pat is either a mother or a father. If Pat is a mother, then she is a parent. If Pat is a father, he is a parent. So, either way, Pat is a parent. (Assume that this conclusion is true.)
9. People who live in the Carolinas live in either North Carolina or South Carolina. Hillary Clinton does not live in North Carolina or South Carolina. Hence, she does not live in the Carolinas.
10. If all of Illinois were in Canada, then Chicago would be in Canada. But Chicago is not in Canada. Therefore, not all of Illinois is in Canada.

Key Concepts

Modus Tollens

Modus tollens is a standard form of deductive argument. It states that if a conditional statement ('if A then B') is accepted and the consequent (B) is found to be false, then the antecedent (A) must also be false. This rule is vital for ensuring that implications are used logically in reasoning.

Disjunctive Reasoning

Disjunctive reasoning deals with statements that offer a choice between mutually exclusive alternatives. By analyzing such 'either/or' scenarios, one can determine the truth of the conclusion when one of the alternatives is eliminated.

Deductive Reasoning

Deductive reasoning involves drawing a specific conclusion from general premises. It ensures that if the premises are true, the conclusion follows with necessity, and it forms the basis for evaluating the validity of arguments.

Validity

Validity refers to the logical structure of an argument—an argument is valid if the conclusion necessarily follows from its premises. It does not depend on the actual truth of the premises, but rather on whether, assuming the premises are true, the conclusion must also be true.

Soundness

Soundness is a property of an argument where it is not only valid but also has all true premises. A sound argument guarantees that the conclusion is true, since its logical form is correct and its starting points are factually accurate.

Logical Fallacies

Logical fallacies are errors in reasoning that weaken an argument. They include deceptive or misleading forms of argumentation that may appear persuasive superficially, but contain flaws in logic that prevent a proper connection between the premises and the conclusion.

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