Question Database: Formal Logic
Propositional Logic: Trees
Caption: If the world looked like this, and you wanted to buy a car that sticks out a little, you probably wouldn't buy a Volkswagen Station Wagon. But in case you haven't noticed, the world doesn't look like this. So if you've wanted to buy a car that sticks out a little, you know just what to do.
Assuming that 'you know just what to do' means 'you will decide to buy a Volkswagen Station Wagon', which one of the following is the most appropriate formalisation of the argument in this ad:
p = The world looks like the ad.
q = You want to buy a car that sticks out a little.
r = You will decide to buy a VW Station Wagon.
A. (p & q) ⊃ ~r, ~p therefore r
B. (p & q) ⊃ ~r, ~p therefore ~r
C. (p & q) ⊃ ~r, ~p therefore q ⊃ r
D. (p & q) ⊃ ~r, ~p therefore ~(q ⊃ r)
Answer: C
Topic:
Trees
Course Level:
First year formal logic
Notes:
Which of the following represents the start of a tree to test the validity of the argument in the ad?
(p & q) ⊃ ~r, ~p therefore q ⊃ r
| A. | B. |
 |
 |
C. |
D. |
 |
 |
Answer: D
Topic:
Trees
Course Level:
First year formal logic
Notes:
Which of the following is one way to continue the tree?
| A. | B. |
 |
 |
C. |
D. |
 |
 |
Answer: B
Topic:
Trees
Course Level:
First year formal logic
Notes:
Which of the following is one way to continue the tree?
| A. | B. |
 |
 |
C. |
D. |
 |
 |
Answer: B
Topic:
Trees
Course Level:
First year formal logic
Notes:
Which of the following is one way to continue the tree?
| A. | B. | C. |
 |
 |
 |
Answer: A
Topic:
Trees
Course Level:
First year formal logic
Notes:
Is the argument valid?
A. Yes
B. No
C. Can’t tell
Answer: B
Topic:
Trees
Course Level:
First year formal logic
Notes:
Which of the following are counter-examples?
A. q = 1, r = 0, p = 0
B. q = 1. r = 0, p = 1
C. Both A and B
D. Neither A nor B
Answer: A
Topic:
Trees
Course Level:
First year formal logic
Notes:
Suppose you have a tree, starting with formulas A, ~B and C, and the tree closes.
This tells you that
A. the argument from A, ~B to C is valid.
B. the argument from A, ~B to C is invalid.
C. the argument from A, C to B is valid.
D. the argument from A, C to B is invalid.
Answer: C
Topic:
Trees
Course Level:
First year formal logic
Notes:
Suppose you want to test whether or not A is a contradiction.
You should
A. do a tree for ~A. If it closes, A is a contradiction.
B. do a tree for A. If it closes, A is a contradiction.
C. do a tree for ~A. If it stays open, A is a contradiction.
D. do a tree for A. If it stays open, A is a contradiction.
Answer: B
Topic:
Trees
Course Level:
First year formal logic