PHIL1250 - Using Venn diagrams, test

Final Exam

Phil 1250

Question 1

Using Venn diagrams, test the following syllogistic forms for validity:

#1. All M is P All P is S ———- All M is S

#2. All M is P All P is S ———- Some M is S

#3. Some P is M Some M is S ———- Some P is S

Question 2

What does it mean for two propositions to be statistically independent? Answer this question by giving both (i) a formal, probabilistic definition, and (ii) a more intuitive definition in your own words.

Question 3

What does it mean for two propositions to be mutually exclusive? Answer this question by giving both (i) a formal, probabilistic definition, and (ii) a more intuitive definition in your own words.

4 Question 4

Can two propositions be both mutually exclusive and independent? Explain your answer.

Question 5

What is the probability of drawing an Ace or a King from a standard fifty-two-card deck, and then (after replacing the card to the deck and reshuffling) drawing another King?

Question 6

If you roll two fair six-sided dice one time, what is the probability that one or the other (or both) of the dice will come up a five or six?

Question 7

Jim, a famous baseball player, tests positive for steriod use in a random screening of all major leaguers. It is known that the test used has a ”true positive” rate (the probability that the test will be positive given that the person does indeed use steroids) of 95% and a ”false positive” rate (the probability that the test will be positive given that the person does not use sterioids) of 10%. Moreover, it is also known that 10% of major leaguers are steroid users. What is the probability that Jim really does use steroids given that he tested positive?

Question 8

Only one of the following statements is true. Which one? A. Every argument that has false premises is invalid. B. Every argument that has all true premises and a true conclusion is valid. C. Every argument that has all true premises and a false conclusion is invalid. D. All of the above statements are actually false.

Question 9

Using a truth-table, test the following argument form for validity:

#1. p v q p ⊃ q q ⊃ r ———- r

#2. ¬(p&q) ¬p ———-¬q

#3. r ———- (p ⊃ q) v (q ⊃ p)

Question 10

Using a truth-table to determine whether the following propositional forms are logically (truth-functionally) equiv- alent to each other. ¬¬(p&q) ¬¬p&¬¬q

Question 11

Using propositional logic (symbols and truth-tables), show whether or not the following two propositions are logically equivalent: If this coffee comes from Alchemy Cafe, then it’s organic. Either this coffee is not from Alchemy Cafe, or it’s organic.

Question 12

Translate each of the following sentences into the language of predicate logic. In other words, reword each sentence explicitly as A, E, I, or O proposition. 1. Mermaids don’t have souls. 2. Shamu is not a fish.

Question 13

First, write out the rule of probability that you will use to answer the following question; Second, use that rule to calculate the probability: Let’s say that you draw two cards from a deck without replacing the first in-between draws. What is the probability of drawing two aces?

Question 14

(a) Calculate the expected monetary value for the following two bets. (b) From the standpoint of expected monetary value, which of these bets would it be more rational to take, and why? (c) which bet would you rather take in real life, and why? 1. I’m going to flip a fair coin. If it lands heads, then I’ll give you $ 100; otherwise, you give me $ 90. 2. I am going to flip a fair coin. If it lands heads, then I’ll give you $1000; otherwise, you give me $ 900.

Question 15

Decide if there are any argument markers in the following sentence. If there are, list the markers(s), and then note whether it’s a reason or conclusion marker: 1. I refuse to take that bet, because I do not care one bit about the prize! 2. I am going to Smith’s; then I am coming home. 3. I still need to stop at Smith’s, so I cannot come home yet.