Philosophy 117 – HOMEWORK ASSIGNMENT #2

Directions: Answer all questions completely according to all the directions given. In addition to your book and notes, you are permitted to work with other students from the class, if you so desire. Direct copying of answers is prohibited, and may result in a 0 grade for the assignment. When you are finished, upload the homework as a MSWord (.docx) or Adobe (.pdf) document to the appropriate assignment in Canvas. If you wish, you may print the homework and scan the completed pages. You may also take photos of the pages and upload them, but be sure your answers are legible.

Section 1: Short Answer. (10 points)

1. Explain the purpose of using parenthesis and/or brackets in symbolic logic.

2. Explain how to determine the truth value of a statement using a truth table.

3. Explain the difference between a main operator and a minor operator in a statement.

4. Provide an example of a vague symbolic statement using at least two operators (e.g. one in which you cannot identify the main operator).

5. Provide an example of a well-formed symbolic statement using at least three operators.

6. Under what condition(s) does the negation operator yield a true statement?

7. Under what condition(s) does the conjunction operator yield a true statement?

8. Under what condition(s) does the conditional (material conditional) operator yield a false statement?

9. Under what condition(s) does the disjunction operator yield a false statement?

10. Under what condition(s) does the biconditional operator yield a false statement?

Section 2: Truth Tables. Directions: Using the variables ‘P’, ‘Q’, and ‘R’, symbolize the following statements and then construct truth tables for them. (40 points)

You may copy and paste the following symbols for your truth tables:

Negation: ?

Disjunction: ?

Conjunction: ?

Conditional: ?

Biconditional: ?

1. Fenrir devoured Odin but Ragnarok did not occur.

2. Lee Harvey Oswald was a pawn if the FBI was responsible for JFK’s death.

3. The fire will ignite if and only if the timber is not wet.

4. It’s not the case that the truth table for this sentence is difficult to construct.

5. If it’s false that Ragnarok occurred, then it’s false that Fenrir devoured Odin.

6. Either Tommy likes to kick dogs in their dumb dog-faces or it is false that he is nice to penguins.

7. Thor’s hammer Mjolnir is nearly indestructible, but once he broke it fighting the Celestial ‘Exitar’.

8. It’s false that you will succeed at logic if and only if you study hard and you attend classes regularly.

9. If you fail to answer this question correctly, then you may have misidentified the main operator and it’s false that you will get a perfect score on this homework.

10. Correctly identifying all the variant instances of negation is confusing, but at least Glen didn’t include any variant instances of conjunction or make you diagram any four variable truth trees.

Section 3: Truth Tables and Validity. Directions: Using the variables ‘A’, ‘B’, and ‘C’ as needed, evaluate the validity of the arguments below by constructing complete truth tables. If the argument is invalid, write INVALID and indicate the truth values of the variables in which the premises are all true and the conclusion is false (e.g. the counterexample row). If there is more than one such row, you only need to indicate one. If the argument is valid, write ‘VALID’. (50 points)

1.

1. If Obama is actually a four dimensional lizard person, then his birth certificate is a phony.

2. Obama is actually a four dimensional lizard person.

3. So, his birth certificate is a phony.

2.

1. If humankind is alone in the universe, then it is false that we will see indication of life in the cosmos.

2. It is false that we will see indication of life in the cosmos.

3. So, humankind is alone in the universe.

3.

1. Students sometimes have a difficult time understanding the logical properties of the inclusive ‘OR’.

2. So, either students sometimes have a difficult time understanding the logical properties of the inclusive ‘OR’, or Donald Trump is actually the late comedian Bill Hicks wearing an elaborate costume.

4.

1. If Santa Claus exists, then everything we’ve learned after the age of five was a lie.

2. If Santa Claus exists, then everything we learned before the age of five was a lie.

3. So, either everything we’ve learned after the age of five was a lie, or everything we learned before the age of five was a lie.

5.

1. If God exists, then either it would be false that there is horrendous evil in the world, or God is, in fact, evil.

2. It is false that there is horrendous evil in the world.

3. So, it is false that God is, in fact, evil.