Formal Logic

Question 1

For any proposition A we can form the negation of that proposition, which simply asserts what?

Answer 1

That A is not true

Question 2

How do we write negation?

Answer 2

‘It’s not true that A’, or ‘A is not true’

Question 3

What is the negation of ‘Birds eat cabbages’?

Answer 3

‘It’s not true that birds eat cabbages.’

Question 4

What two things must the sentence and its negation be?

Answer 4

Inconsistent and exhaustive

Question 5

Define inconsistent.

Answer 5

Incompatible - both cannot be true

Question 6

Define exhaustive.

Answer 6

No other possibilities - cannot both be false

Question 7

What aren’t the sentences ‘wild mushrooms are delicious’ and ‘wild mushrooms are dangerous’?

Answer 7

Not inconsistent - they can both be true

Question 8

What aren’t the sentences ‘That bird is a crow’ and ‘That bird is a raven’?

Answer 8

Not exhaustive - they can both be false

Question 9

Give an example of a conditional.

Answer 9

‘If it’s raining then I should take my umbrella’

Question 10

For any two proposition A and B, how do we write it as a conditional?

Answer 10

If A then B

Question 11

‘If A then B’ is what?

Answer 11

A proposition

Question 12

What is a proposition?

Answer 12

Something that can be true or false

Question 13

Whether a particular sentence with the form ‘If A then B’ is true or false depends on what?

Answer 13

Whether A and B are true or false

Question 14

What is the ‘IF’ part of the sentence called?

Answer 14

The antecedent

Question 15

What should you think of the antecedent as?

Answer 15

A condition that may or may not be satisfied

Question 16

What is the ‘THEN’ part of the sentence called?

Answer 16

The consequent

Question 17

What should you think of the consequent as?

Answer 17

Something that supposedly follows from that condition

Question 18

What does the condition ‘If A then B’ not say?

Answer 18

That A is true, and it doesn’t say that B is true

Question 19

What does the conditional ‘If A then B’ assert?

Answer 19

The relationship between A and B

Question 20

Sometimes we use an ‘If… Then…’ sentence when A does what to B?

Answer 20

When A causes or influences B.
E.g. ‘If it rains then I’ll stay at home’
‘If you drink more coffee then you won’t sleep well’

Question 21

Sometimes we use ‘If… then…’ to show what?

Answer 21

That the direction of causation goes from B to A
E.g. ‘If my keys aren’t here then I left them at home’
‘If these fingerprints match then you’re guilty’

Question 22

Sometimes there no direct what between A and B?

Answer 22

Sometimes there’s no direct cause or physical relation between them at all
E.g. ‘If the thermometer goes up then I’ll buy ice-cream’

Question 23

What is the best way to think of ‘If A then B’?

Answer 23

‘Knowing that A was true would tell you that B is true’

Question 24

Give the formalised version of modus ponens argument.

Answer 24

P1: If A then B
P2: A
Conc: B

Question 25

Give the formalised version of modus tollens argument.

Answer 25

P1: If A then B
P2: B is not true
Conc: A is not true

Question 26

Give an example of modus tollens.

Answer 26

P1: If there’s an elephant in the room then we can see an elephant
P2: It’s not true that we can see an elephant
Conc: It’s not true that there’s an elephant in the room

Question 27

Is the following argument valid? What is this called?
P1: If A then B
P2: B
Conc: A

Answer 27

This is invalid and is called affirming the consequent

Question 28

Is the following argument valid? What is this called?
P1: If A then B
P2: A is not true
Conc: B is not true

Answer 28

This is invalid and is called denying the antecedent

Question 29

Give an example of affirming the consequent.

Answer 29

P1: If it’s raining then the windows are wet
P2: The windows are wet
Conc: It’s raining

Question 30

Give an example of denying the antecedent.

Answer 30

P1: If it’s raining then the windows are wet
P2: It’s not true that it’s raining
Conc: It’s not true that the windows are wet

Question 31

What are logic operators sometimes also called?

Answer 31

Logical connective

Question 32

What is the logical operator for A and B?

Answer 32

&

Question 33

What is the logical operator for A or B?

Answer 33

V

Question 34

What is the logical operator for If A then B?

Answer 34

=>

Question 35

What is the logical operator for It’s not true that A?

Answer 35

¬

Question 36

What is the difference between arithmetic operators and logical operators?

Answer 36

The latter don’t act on numbers but sentences

Question 37

We can think of sentences here as what?

Answer 37

Truth values

Question 38

What are truth values?

Answer 38

Whether or not a proposition is true or false

Question 39

How do we write truth values?

Answer 39

T for true; F for false

Question 40

Given two propositions ‘A’ and ‘B’ what sentence can we form with conjunction?

Answer 40

A&B

Question 41

A&B is true when?

Answer 41

When both A and B are true

Question 42

If we know the truth value of either A or B, then we can do what?

Answer 42

Tell whether A&B is true or false.

Question 43

What are the four possibilities we have to consider with A&B?

Answer 43

T T | T
T F | F
F T | F
F F | F

Question 44

What does this do?
A B | A&B
—————
T T | T
T F | F
F T | F
F F | F

Answer 44

Show that the sentences are not related or relevant to each other

Question 45

Give two propositions ‘A’ and ‘B’ what sentence can we form with disjunction?

Answer 45

AVB

Question 46

A V B is true when what?

Answer 46

At least one of A and B are true

Question 47

So, if we know the truth value of A, we know what?

Answer 47

Whether A V B is true

Question 48

What are the four possibilities we have to consider with A V B?

Answer 48

T T | T
T F | T
F T | T
F F | F

Question 49

What does this do?
A B | AVB
—————
T T | T
T F | T
F T | T
F F | F

Answer 49

Show that A V B is inclusive and that the truth of A V B does not tell us of the truth of the individual propositions

Question 50

Given the proposition ‘A’ we can form what with negation?

Answer 50

¬A

Question 51

¬A is true when?

Answer 51

A is false

Question 52

What are the two possibilities we have to consider with ¬A

Answer 52

T | F
F | T

Question 53

Given two propositions A and B, we can form what with the conditional?

Answer 53

A=>B

Question 54

What are the four possibilities we have to consider with A=>B?

Answer 54

T T | T
T F | F
F T | T
F F | T