Lesson test: Truth tables

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Truth tables

1.[2p]
How many rows does a truth table with six atoms have?

CorrectNot quite: 64

2.[2p]
An argument is shown to be invalid by a truth table when

some row makes every premise true and the conclusion false

Correct

some row makes every premise false

The answer is: some row makes every premise true and the conclusion false

no row makes the conclusion true

The answer is: some row makes every premise true and the conclusion false

some row makes the conclusion false

The answer is: some row makes every premise true and the conclusion false

3.[2p]
What is a formula called when it is true in every row of its table?

CorrectNot quite: tautology

4.[3p]
In how many of the eight rows is $P \to (Q \lor R)$ true?

CorrectNot quite: 7

5.[3p]
Match each formula to its classification.

$P \lor \neg P$
$P \land \neg P$
$P \to Q$
$(P \to Q) \lor (Q \to P)$

contingency
contradiction
tautology
tautology

Show the answer

$P \lor \neg P$ : tautology $P \land \neg P$ : contradiction $P \to Q$ : contingency $(P \to Q) \lor (Q \to P)$ : tautology

6.[2p]
The set $P$ , $P \to Q$ , $\neg Q$ is consistent.

True

The answer is: False

False

Correct

7.[3p]
Which argument is valid?

$P \lor Q$ , $\neg P$ , therefore $Q$

Correct

$P \to Q$ , $Q$ , therefore $P$

The answer is: $P \vee Q$, $\neg P$, therefore $Q$

$P \to Q$ , $\neg P$ , therefore $\neg Q$

The answer is: $P \vee Q$, $\neg P$, therefore $Q$

$P \lor Q$ , $P$ , therefore $\neg Q$

The answer is: $P \vee Q$, $\neg P$, therefore $Q$

8.[2p]
An inconsistent set of premises entails every formula.

True

Correct

False

The answer is: True

9.[3p]
Why does the short cut start by assuming the conclusion is false?

It is the only way a counterexample row can look, so the search can be driven backwards from it

Correct

It proves the conclusion is false

The answer is: It is the only way a counterexample row can look, so the search can be driven backwards from it

It halves the number of atoms

The answer is: It is the only way a counterexample row can look, so the search can be driven backwards from it

It makes every premise true automatically

The answer is: It is the only way a counterexample row can look, so the search can be driven backwards from it

1.[2p] How many rows does a truth table with six atoms have?

2.[2p] An argument is shown to be invalid by a truth table when

3.[2p] What is a formula called when it is true in every row of its table?

4.[3p] In how many of the eight rows is P→(Q∨R) true?

5.[3p] Match each formula to its classification.

6.[2p] The set P, P→Q, ¬Q is consistent.

7.[3p] Which argument is valid?

8.[2p] An inconsistent set of premises entails every formula.

9.[3p] Why does the short cut start by assuming the conclusion is false?

1.[2p]
How many rows does a truth table with six atoms have?

2.[2p]
An argument is shown to be invalid by a truth table when

3.[2p]
What is a formula called when it is true in every row of its table?

4.[3p]
In how many of the eight rows is $P \to (Q \lor R)$ true?

5.[3p]
Match each formula to its classification.

6.[2p]
The set $P$ , $P \to Q$ , $\neg Q$ is consistent.

7.[3p]
Which argument is valid?

8.[2p]
An inconsistent set of premises entails every formula.

9.[3p]
Why does the short cut start by assuming the conclusion is false?