Examination Questions And Answers English Work Sheet (Page 5 of 7) in pdf

Examination Questions And Answers English Work Sheet Page 5

C. Translating

Translate the following into more or less colloquial English sentences. Let J = “Art gets

a new job”; B = “Art gets a new boss”; A = “Art gets a new apartment”; R = “Art get a

new roommate.”

1. ~ (J ∨ B)

~ J ⊃ ~ [(B ∨ (A ∨ R)]

2. J ⊃ (B ⋅ A)

(~ A ∨ ~ R) ⊃ ~ J

3. ~ (A ⋅ R)

(B ≡ J) ⋅ (R ≡ A)

C. Answers

1. Art will get neither a new job nor a new boss.

2. If Art gets a new job then he will get a new boss and a new apartment.

3. Art will not get both a new apartment and a new roommate.

4. If Art does not get a new job, then he will get neither a new boss, nor a new

apartment, nor a new roommate.

5. If Art either does not get a new apartment or does not get a new roommate, then he

does not get a new job.

6. Art gets a new boss if and only if he gets a new job, and a new roommate just in

case he gets a new apartment.

III. CHAPTER THREE: TRUTH TABLES

A. General Theory

Determine the sentence forms of which the following are substitution instances:

~ (A ≡ B) ⊃ C

b. A ∨ (B ⋅ ~ C)

If a sentence form contains five variables, how many lines or rows must its

complete truth table analysis have?

Assume you know of an argument only that its premises are not consistent. What,

if anything, can you tell about the argument’s validity? (Defend your answer.)

Why is it true that any argument with a conclusion with the form p ∨ ~ p is valid?

a. We can define a tautologous sentence as one that is a substitution instance of

some tautologous sentence form, and a contradictory sentence as one that is a

substitution instance of some contradictory sentence form. Why can’t we

analogously define a contingent sentence as one that is a substitution instance of

some contingent sentence form? (Defend your answer, including examples.)

b. We cannot define a contingent sentence as one that is a substitution instance

of some contingent sentence form. But then how can we define that term?

Examination Questions And Answers English Work Sheet Page 5