Logic 103 Exam 2

Which of the following is a simple statement?
A) Moe is a dog but he acts like a human.
B) Moe is a dog, whereas Sasha is a cat.
C) Sasha is hungry because Willa ate Sasha’s dinner.
D) This exam is easy.

Consider the following: If those roller skates hadn’t been on the stairs, she would not have tripped. What kind of conditional is this?
A) indicative
B) counterfactual/subjunctive,
C) logically equivalent,
D) material,

Which of the following is most obviously not a truth-functional statement?
A) The Earth is 13.7 billion years old.
B) The Earth is either 13.7 billion years old or grass is green.
C) The Earth is 13.7 billion years old but grass is not green.
D) Frank believes that the Earth is 13.7 billion years old.

Which of the following is not one of the three “Laws of Thought”?
A) (p ⊃ p) is always true,
B) (p v ~p) is always true,
C) (p ⊃ ~p) is always false
D) (p • ~p) is always false,

Which of the following is NOT true? A: ~(x)Fx⇔(∃x)~Fx. B: (x)Fx⇔~(∃x)~Fx. C: ~(x)~Fx⇔(∃x)Fx. D: (x)~Fx⇔~(∃x)Fx. E: all of the above. F: none of the above.

Symbolize the following statement, using capital letters to abbreviate the simple statements involved: Argentina will mobilize only if Brazil protests to the U.N., while Chile will call for a meeting of all of the Latin American states if the Dominican Republic does not call for such a meeting.

Symbolize the following statement, using capital letters to abbreviate the simple statements involved: If oil consumption continues to grow, then either oil imports will increase or domestic oil reserves will be depleted. If oil imports increase and domestic oil reserves are depleted, then, unless a new source of income is found, the nation will go bankrupt. Therefore, the nation will go bankrupt if and only if oil consumption continues to grow.

The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. (S≡T) v [Q ⊃ (O • R)] 2. ~(S≡T) 3. [Q ⊃ (O • R)]

The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. [N ⊃ (O • P)] • [Q ⊃ (O • R)] 2. N v Q 3. (O • P) v (Q • R)

The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. [T v (U ⊃ S)] • [(W •~V) ⊃ ~T] 2. [T v (U ⊃ S)] • [W ⊃ (~V ⊃ ~T)]

The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. [(W • Z) ⊃ (Y ⊃ Z)] ≡ (~X v Y) 2. {[(W • Z) ⊃ (Y ⊃ Z)] ≡ (~X v Y)} v B

The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. (~A ⊃ B) ⊃ (~C v ~D) 2. (~A ⊃ B) ⊃~(C • D)

The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. (~F v G) • (H ≡ I) 2. (F ⊃ G) • (H ≡ I)

The following is a valid argument. State the rule of inference by which its conclusion follows from its premise or premises. 1. (C v D) ⊃ [(J v K) ⊃ (J • K)] 2. ~[(J v K) ⊃ (J • K)] 3. ~(C v D)

The following is a correct proof. Justify each line that is not a premise with the rule of inference and the line from which it came. 1. (A ⊃ B), 2. (C ⊃~B), ∴ (A ⊃ ~C), 3. (~~B ⊃~C), 4. (B ⊃~C), 5. (A ⊃~C)

Use natural deduction to prove the following: 1. (~A ⊃ A), ∴ A