Lesson test: Predicates and quantifiers

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Predicates and quantifiers

1.[2p]
"All ravens are black" translates as

$\forall x (R x \to B x)$

Correct

$\forall x (R x \land B x)$

The answer is: $\forall x (Rx \rightarrow Bx)$

$\exists x (R x \to B x)$

The answer is: $\forall x (Rx \rightarrow Bx)$

$\exists x (R x \land B x)$

The answer is: $\forall x (Rx \rightarrow Bx)$

2.[2p]
"Some ravens are black" translates as

$\exists x (R x \land B x)$

Correct

$\exists x (R x \to B x)$

The answer is: $\exists x (Rx \wedge Bx)$

$\forall x (R x \land B x)$

The answer is: $\exists x (Rx \wedge Bx)$

$\forall x (R x \to B x)$

The answer is: $\exists x (Rx \wedge Bx)$

3.[3p]
What is wrong with writing "some ravens are black" as $\exists x (R x \to B x)$ ?

A single non-raven in the domain makes it true, whatever ravens are like

Correct

It says every raven is black

The answer is: A single non-raven in the domain makes it true, whatever ravens are like

It has a free variable

The answer is: A single non-raven in the domain makes it true, whatever ravens are like

It cannot be evaluated without a name

The answer is: A single non-raven in the domain makes it true, whatever ravens are like

4.[3p]
Match each categorical form to its translation.

All F are G
No F is G
Some F is G
Some F is not G

$\exists x (F x \land \neg G x)$
$\forall x (F x \to G x)$
$\forall x (F x \to \neg G x)$
$\exists x (F x \land G x)$

Show the answer

All F are G: $\forall x (F x \to G x)$ No F is G: $\forall x (F x \to \neg G x)$ Some F is G: $\exists x (F x \land G x)$ Some F is not G: $\exists x (F x \land \neg G x)$

5.[3p]
Of the 256 categorical syllogism forms, how many are valid under modern semantics, with no assumption that the terms are non-empty?

CorrectNot quite: 15

6.[2p]
How many are valid once every term is assumed to name at least one thing?

CorrectNot quite: 24

7.[2p]
"Every unicorn in this room is on fire" is true in a room with no unicorns.

True

Correct

False

The answer is: True

8.[3p]
Which formula is not a sentence?

$\forall x F x \to G x$

Correct

$\forall x (F x \to G x)$

The answer is: $\forall x\, Fx \rightarrow Gx$

$\exists x (F x \land G x)$

The answer is: $\forall x\, Fx \rightarrow Gx$

$F s \to G s$

The answer is: $\forall x\, Fx \rightarrow Gx$

9.[2p]
$\neg \forall x F x$ and $\forall x \neg F x$ differ because

the first says not everything is $F$ , the second that nothing is

Correct

the first has a free variable

The answer is: the first says not everything is $F$, the second that nothing is

the second is never true

The answer is: the first says not everything is $F$, the second that nothing is

they differ only in notation

The answer is: the first says not everything is $F$, the second that nothing is

1.[2p] "All ravens are black" translates as

2.[2p] "Some ravens are black" translates as

3.[3p] What is wrong with writing "some ravens are black" as ∃x(Rx→Bx)?

4.[3p] Match each categorical form to its translation.

5.[3p] Of the 256 categorical syllogism forms, how many are valid under modern semantics, with no assumption that the terms are non-empty?

6.[2p] How many are valid once every term is assumed to name at least one thing?

7.[2p] "Every unicorn in this room is on fire" is true in a room with no unicorns.

8.[3p] Which formula is not a sentence?

9.[2p] ¬∀xFx and ∀x¬Fx differ because

1.[2p]
"All ravens are black" translates as

2.[2p]
"Some ravens are black" translates as

3.[3p]
What is wrong with writing "some ravens are black" as $\exists x (R x \to B x)$ ?

4.[3p]
Match each categorical form to its translation.

5.[3p]
Of the 256 categorical syllogism forms, how many are valid under modern semantics, with no assumption that the terms are non-empty?

6.[2p]
How many are valid once every term is assumed to name at least one thing?

7.[2p]
"Every unicorn in this room is on fire" is true in a room with no unicorns.

8.[3p]
Which formula is not a sentence?

9.[2p]
$\neg \forall x F x$ and $\forall x \neg F x$ differ because