Question Database: Formal Logic
Truth Tables
Decide if the formula ~((p & q) ≡ p) is a
A. tautology
B. contradiction
C. contingency
Answer: C
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
For these questions, ask the students to write out their own truth-table for the formula. (Allow them to refer to their notes or the text book). Given them 3-4 minutes to do that. Then get them to give their answers using the cards. If there is enough disagreement, get them to swap their working with someone sitting nearby, and see if they can spot any mistakes.
Decide if the formula ~(p ∨ (q ⊃ ~p)) is a
A. tautology
B. contradiction
C. contingency
Answer: B
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
Decide if the formula (p ∨ q) ≡ (p ⊃ q) ⊃ q is a
A. tautology
B. contradiction
C. contingency
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
Decide if the formula (p ⊃ q) ⊃ ~(q ⊃ p) is a
A. tautology
B. contradiction
C. contingency
Answer: C
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
Suppose the statements a and b are true, f and g are false and that p and q have unknown truth value. What can you say about the truth value of the following compund propositions?
p & f
A. True
B. False
C. Cannot be determined
Answer: B
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
Second conjunct is false
Suppose the statements a and b are true, f and g are false and that p and q have unknown truth value. What can you say about the truth value of the following compund propositions?
~(p ∨ a)
A. True
B. False
C. Cannot be determined
Answer: B
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
Second disjunct true, so formula is false.
Suppose the statements a and b are true, f and g are false and that p and q have unknown truth value. What can you say about the truth value of the following compund propositions?
(~b ⊃ p) ∨ (a & (~q ≡ f))
A. True
B. False
C. Cannot be determined
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
False antecedent, so left disjunct true.
Suppose the statements a and b are true, f and g are false and that p and q have unknown truth value. What can you say about the truth value of the following compund propositions?
~p ⊃ b
A. True
B. False
C. Cannot be determined
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
True consequent.
Suppose the statements a and b are true, f and g are false and that p and q have unknown truth value. What can you say about the truth value of the following compund propositions?
[(p ≡ f) & (a ⊃ f)] ∨ [~p ∨ q]
A. True
B. False
C. Cannot be determined
Answer: C
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
a ⊃ f must be false, so conjunction is false. But truth value of the right disjunct cannot be determined.
Truth tables for arguments
Look at this argument and dictionary:
If the printer is unplugged or the ink cartridge is empty, the page will not print. The page did not print. Therefore the printer is not plugged in.
p = the printer is plugged in.
c = the ink cartridge is empty.
g = the page was printed.
which is the best formalisation?
A. (p ∨ c) ⊃ ~g, g therefore ~p
B. (p ∨ ~c) ⊃ ~g, g therefore ~p
C. (~p ∨ c) ⊃ ~g, ~g therefore ~p
D. (~p ∨ c) ⊃ g, ~g therefore p
Answer: C
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
What truth values go in the missing spaces in the truth table for this argument?
What goes in space V?
A. 1
B. 0
(~p ∨ c) ⊃ ~g, ~g therefore ~p
|
p |
c |
g |
|
(~p |
∨ |
c ) |
⊃ |
~g |
|
~g |
~p |
| ||||||||||||
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
1 |
1 |
|
1 |
1 |
2 |
0 |
0 |
1 |
|
1 |
1 |
0 |
Z |
0 |
|
0 |
1 |
3 |
0 |
1 |
0 |
|
1 |
1 |
1 |
1 |
1 |
|
1 |
1 |
4 |
0 |
1 |
1 |
|
1 |
1 |
1 |
0 |
0 |
|
0 |
1 |
5 |
1 |
0 |
0 |
|
0 |
X |
0 |
Y |
1 |
|
1 |
0 |
6 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
7 |
1 |
1 |
0 |
|
0 |
V |
1 |
W |
1 |
|
1 |
0 |
8 |
1 |
1 |
1 |
|
0 |
1 |
1 |
0 |
0 |
|
0 |
0 |
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
What truth values go in the missing spaces in the truth table for this argument?
What goes in space W?
A. 1
B. 0
|
p |
c |
g |
|
(~p |
∨ |
c ) |
⊃ |
~g |
|
~g |
~p |
| ||||||||||||
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
1 |
1 |
|
1 |
1 |
2 |
0 |
0 |
1 |
|
1 |
1 |
0 |
Z |
0 |
|
0 |
1 |
3 |
0 |
1 |
0 |
|
1 |
1 |
1 |
1 |
1 |
|
1 |
1 |
4 |
0 |
1 |
1 |
|
1 |
1 |
1 |
0 |
0 |
|
0 |
1 |
5 |
1 |
0 |
0 |
|
0 |
X |
0 |
Y |
1 |
|
1 |
0 |
6 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
7 |
1 |
1 |
0 |
|
0 |
1 |
1 |
W |
1 |
|
1 |
0 |
8 |
1 |
1 |
1 |
|
0 |
1 |
1 |
0 |
0 |
|
0 |
0 |
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
What truth values go in the missing spaces in the truth table for this argument?
What goes in space X?
A. 1
B. 0
|
p |
c |
g |
|
(~p |
∨ |
c ) |
⊃ |
~g |
|
~g |
~p |
| ||||||||||||
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
1 |
1 |
|
1 |
1 |
2 |
0 |
0 |
1 |
|
1 |
1 |
0 |
Z |
0 |
|
0 |
1 |
3 |
0 |
1 |
0 |
|
1 |
1 |
1 |
1 |
1 |
|
1 |
1 |
4 |
0 |
1 |
1 |
|
1 |
1 |
1 |
0 |
0 |
|
0 |
1 |
5 |
1 |
0 |
0 |
|
0 |
X |
0 |
Y |
1 |
|
1 |
0 |
6 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
7 |
1 |
1 |
0 |
|
0 |
1 |
1 |
1 |
1 |
|
1 |
0 |
8 |
1 |
1 |
1 |
|
0 |
1 |
1 |
0 |
0 |
|
0 |
0 |
Answer: B
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
What truth values go in the missing spaces in the truth table for this argument?
What goes in space Y?
A. 1
B. 0
|
p |
c |
g |
|
(~p |
∨ |
c ) |
⊃ |
~g |
|
~g |
~p |
| ||||||||||||
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
1 |
1 |
|
1 |
1 |
2 |
0 |
0 |
1 |
|
1 |
1 |
0 |
Z |
0 |
|
0 |
1 |
3 |
0 |
1 |
0 |
|
1 |
1 |
1 |
1 |
1 |
|
1 |
1 |
4 |
0 |
1 |
1 |
|
1 |
1 |
1 |
0 |
0 |
|
0 |
1 |
5 |
1 |
0 |
0 |
|
0 |
0 |
0 |
Y |
1 |
|
1 |
0 |
6 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
7 |
1 |
1 |
0 |
|
0 |
1 |
1 |
1 |
1 |
|
1 |
0 |
8 |
1 |
1 |
1 |
|
0 |
1 |
1 |
0 |
0 |
|
0 |
0 |
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
What truth values go in the missing spaces in the truth table for this argument?
What value goes in space Z?
A. 1
B. 0
|
p |
c |
g |
|
(~p |
∨ |
c ) |
⊃ |
~g |
|
~g |
~p |
| ||||||||||||
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
1 |
1 |
|
1 |
1 |
2 |
0 |
0 |
1 |
|
1 |
1 |
0 |
Z |
0 |
|
0 |
1 |
3 |
0 |
1 |
0 |
|
1 |
1 |
1 |
1 |
1 |
|
1 |
1 |
4 |
0 |
1 |
1 |
|
1 |
1 |
1 |
0 |
0 |
|
0 |
1 |
5 |
1 |
0 |
0 |
|
0 |
0 |
0 |
1 |
1 |
|
1 |
0 |
6 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
7 |
1 |
1 |
0 |
|
0 |
1 |
1 |
1 |
1 |
|
1 |
0 |
8 |
1 |
1 |
1 |
|
0 |
1 |
1 |
0 |
0 |
|
0 |
0 |
Answer: B
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
The truth table shows that the argument is:
A. Valid
B. Invalid
C. Impossible to tell
|
p |
c |
g |
|
(~p |
∨ |
c ) |
⊃ |
~g |
|
~g |
~p |
| ||||||||||||
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
1 |
1 |
|
1 |
1 |
2 |
0 |
0 |
1 |
|
1 |
1 |
0 |
0 |
0 |
|
0 |
1 |
3 |
0 |
1 |
0 |
|
1 |
1 |
1 |
1 |
1 |
|
1 |
1 |
4 |
0 |
1 |
1 |
|
1 |
1 |
1 |
0 |
0 |
|
0 |
1 |
5 |
1 |
0 |
0 |
|
0 |
0 |
0 |
1 |
1 |
|
1 |
0 |
6 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
7 |
1 |
1 |
0 |
|
0 |
1 |
1 |
1 |
1 |
|
1 |
0 |
8 |
1 |
1 |
1 |
|
0 |
1 |
1 |
0 |
0 |
|
0 |
0 |
Answer: B
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
Counter-examples to the validity of this argument are found on lines:
A. 5 only
B. 5 and 6
C. 1 and 3
D. 5 and 7
Answer: D
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
Indirect truth table method
Look at this part of a row of a truth-table:
(~ p |
∨ |
c) |
⊃ |
~ g |
, |
~ g |
|
~ p |
1 |
|
1 |
0 ? |
1. What value goes in the marked slot?
A. 0
B. 1
C. Can't tell.
Answer: B
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
(~ p |
∨ |
c) |
⊃ |
~ g |
, |
~ g |
|
~ p |
1 |
|
1 ? |
0 1 |
2. What value goes in the marked slot?
A. 0
B. 1
C. Can't tell.
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
(~ p |
∨ |
c) |
⊃ |
~ g |
, |
~ g |
|
~ p |
1 |
? |
|
1 0 |
0 1 |
3. What value goes in the marked slot?
A. 0
B. 1
C. Can't tell.
Answer: B
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
(~ p |
∨ |
c) |
⊃ |
~ g |
, |
~ g |
therefore |
~ p |
? |
1 |
1 0 |
|
1 0 |
0 1 |
4. What value goes in the marked slot?
A. 0
B. 1
C. Can't tell.
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
(~ p |
∨ |
c) |
⊃ |
~ g |
, |
~ g |
therefore |
~ p |
0 1 |
? |
1 |
1 0 |
|
1 0 |
0 1 |
5. What value goes in the marked slot?
A. 0
B. 1
C. Can't tell.
Answer: C
Topic:
Truth-tables
Course Level:
First year formal logic
Notes:
(~ p |
∨ |
c) |
⊃ |
~ g |
, |
~ g |
therefore |
~ p |
0 1 |
|
1 |
1 0 |
|
1 0 |
0 1 |
What can we conclude about the argument form:
(~p ∨ c) ⊃ ~g , ~g therefore ~p
A. The argument form is invalid.
B. The argument form is invalid.
C. Can't tell.
Answer: A
Topic:
Truth-tables
Course Level:
First year formal logic