Phil 60 – Anderson Third Homework (Due Thur. Feb. 25)

Fall 06

1. Which of the following are truth-functional conjunctions that can be symbolized using the ampersand:

(a) Howard and Estelle are husband and wife.

(b) In the fifties gambling was legal only in Nevada, but now gambling is everywhere.

(c) Sixteen and forty-three are fifty-nine.

2. Assume that whenever it is snowing, the streets and sidewalks are wet and slippery. Given that assumption, which (if any) of the following must be true:

(a) If the sidewalks and streets are slippery and wet, then it is snowing.

(b) If it is not snowing, the streets and sidewalks are not slippery.

(c) If the sidewalks are wet or the streets are slippery, it is snowing.

(d) If the sidewalks are slippery but the streets are dry, it is now snowing.

(e) It is snowing and the sidewalks and streets are wet and slippery.

3. Logically speaking, the type of statement one makes is determined by the main connective. Circle the main connective in the following sentences.

(a) ~ ~ (A v B) → C

(b) ~ [(A v B) v (C → D)]

(c) {[~ (A → B) v C)] ↔ ~ D} v L

(d) [(C → Q) → ~R] → Q

4. Translate into symbols, using the indicated abbreviations.

(a) My client may have had a motive, but he had neither the means nor the opportunity to commit the crime. (C = My client had a motive to commit the crime. M = My client had the means to commit the crime. O = My client had the opportunity to commit the crime.)

(b) Neither stocks nor bonds provide an absolutely risk-free investment opportunity.

(S = Stocks provide an absolutely risk-free investment opportunity. B = Bonds provide an absolutely risk-free investment opportunity.)

(c) Harry will run for office only if Janet runs also. (H = Harry will run. J = Janet will run.)

(d) Janet won’t run for office unless Harry runs as well.

(e) If everything is perfect, I neither make mistakes nor can I be blamed for them.

(E = Everything is perfect. M = I make mistakes. B = I can be blamed for my mistakes.)

(f) If nothing is perfect and I make mistakes, then I can be blamed for them.

(g) If Art neither diets nor exercises, he will gain weight. (D = Art diets. E = Art exercises. G = Art gains weight.)

(h) Art neither diets nor exercises, but he still does not gain weight.

(i) If his heart stops beating, then the patient will live if the doctors apply electric shock.

(S = His heart stops beating. L = The patient will live. E = The doctors apply electric shock.)

(j) Jones will graduate whether or not he pays his tuition. (G = Jones will graduate.

T = Jones pays his tuition.)

5. Translate into readable English. Let R = You should buy real estate. S = You should buy common stocks. M = You should invest in a mutual fund. L = Interest rates are low. E = The economy is in a recession. D = Demand is high. K = You are a knowledgeable investor. P = You are a psychic.

(a) (D & L) → ~E

(b) ~E → (R & S)

(c) S ↔ (K & ~E)

(d) ~ (K v P) → (E → ~S)

(e) [(E & L) & ~K] → M

6. Show by a truth table that the following sentence is a tautology: P → (Q → P).

7. Do Problems 3 and 4 in Section V on page 79 of the text.