Lesson test: The language of propositions

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The language of propositions

1.[2p]
What is the main connective of $\neg (P \land Q) \to (R \lor S)$ ?

The arrow

Correct

The negation

The answer is: The arrow

The conjunction

The answer is: The arrow

The disjunction

The answer is: The arrow

2.[3p]
"You may board only if you hold a ticket" translates as

$B \to T$

Correct

$T \to B$

The answer is: $B \to T$

$B \land T$

The answer is: $B \to T$

$B \leftrightarrow T$

The answer is: $B \to T$

3.[1p]
In this notation, " $P$ or $Q$ " is true when both $P$ and $Q$ are true.

True

Correct

False

The answer is: True

4.[3p]
Which English connective is not truth-functional?

She resigned because the audit failed

Correct

She is qualified but inexperienced

The answer is: She resigned because the audit failed

The flight leaves unless the fog thickens

The answer is: She resigned because the audit failed

Neither the valve nor the pump was replaced

The answer is: She resigned because the audit failed

5.[3p]
Match each English form to its translation.

Neither P nor Q
Not both P and Q
P unless Q
P if Q

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

Show the answer

Neither P nor Q: $\neg P \land \neg Q$ Not both P and Q: $\neg (P \land Q)$ P unless Q: $\neg Q \to P$ P if Q: $Q \to P$

6.[2p]
Which of these are correctly translated as a conjunction?

Select all that apply

She is qualified but inexperienced

Correct

The engine started, although the oil was low

Correct

The report is late; the figures are wrong

Correct

The alarm sounds unless the key is turned

The answer is: She is qualified but inexperienced, The engine started, although the oil was low, The report is late; the figures are wrong

7.[2p]
What is the term for the part of $P \to Q$ that $P$ occupies?

CorrectNot quite: antecedent

8.[2p]
$\neg P \land Q$ and $\neg (P \land Q)$ say the same thing.

True

The answer is: False

False

Correct

9.[2p]
Why does propositional logic treat "Socrates is a man" as a single letter?

It contains no smaller statement, so this language can see no structure in it

Correct

It is too short to analyse

The answer is: It contains no smaller statement, so this language can see no structure in it

Its truth value is unknown

The answer is: It contains no smaller statement, so this language can see no structure in it

Names are not allowed in logic

The answer is: It contains no smaller statement, so this language can see no structure in it

1.[2p] What is the main connective of ¬(P∧Q)→(R∨S)?

2.[3p] "You may board only if you hold a ticket" translates as

3.[1p] In this notation, "P or Q" is true when both P and Q are true.

4.[3p] Which English connective is not truth-functional?

5.[3p] Match each English form to its translation.

6.[2p] Which of these are correctly translated as a conjunction?

7.[2p] What is the term for the part of P→Q that P occupies?

8.[2p] ¬P∧Q and ¬(P∧Q) say the same thing.

9.[2p] Why does propositional logic treat "Socrates is a man" as a single letter?

1.[2p]
What is the main connective of $\neg (P \land Q) \to (R \lor S)$ ?

2.[3p]
"You may board only if you hold a ticket" translates as

3.[1p]
In this notation, " $P$ or $Q$ " is true when both $P$ and $Q$ are true.

4.[3p]
Which English connective is not truth-functional?

5.[3p]
Match each English form to its translation.

6.[2p]
Which of these are correctly translated as a conjunction?

7.[2p]
What is the term for the part of $P \to Q$ that $P$ occupies?

8.[2p]
$\neg P \land Q$ and $\neg (P \land Q)$ say the same thing.

9.[2p]
Why does propositional logic treat "Socrates is a man" as a single letter?