Formal Logic, And, Not, If Then

Question 1

What symbol do we use for ‘and’?

Answer 1

&

Question 2

What type of logical operator is ‘and’?

Answer 2

A conjunction, binary

Question 3

What is the truth table for ‘&’?

Answer 3

A¦ B¦ A&B ¦
T¦ T¦ T ¦
T¦ F¦ F ¦
F¦ T¦ F ¦
F¦ F¦ F ¦

Question 4

What are some synonyms of ‘and’?

Answer 4

‘also’, ‘but’, ‘as well’, ‘however’, ‘and yet’, ‘too’, ‘moreover’, ‘additionally’

They have the same truth table, and also meaning. Sounds different because they have different rhetorical force

Question 5

What symbol do we use for ‘not’?

Answer 5

~

Question 6

What type of logical operator is ‘not’?

Answer 6

negation, singulary

Question 7

What’s a less ambiguous way of saying ‘not’?

Answer 7

It is not the case that…

Question 8

What are some other synonyms of ‘not’?

Answer 8

‘it is not the case that’, ‘neither..nor’, ‘un-‘ (e.g. unapologetic = not apologetic)

Question 9

What is the truth table for ‘~’

Answer 9

A¦~A¦
T¦ F¦
F¦ T¦

Question 10

What does the double negation elimination rule mean?

Answer 10

~~A = A

or in standard form:

P1 ~~A
_____________
C A

Question 11

What does the bad style of argument, an appeal to ignorance look like?

Answer 11

‘We don’t know whether A is true, so A is false (or neither true nor false)’

Question 12

Give an example of an appeal to ignorance (bad) argument?

Answer 12

P1: It has not been determinately show whether there is a planet orbiting Alpha Centauri A
__________________________________________
C1: There is no such planet
C2: P1 is neither true nor false

It is true or false but we simply don’t know

Question 13

What symbol do we use for ‘If-then’?

Answer 13

->

Question 14

What type of logical operator is ‘If-then’?

Answer 14

Conditional

Question 15

What are some synonyms of ‘if then’?

Answer 15

‘if’, ‘only if’, ‘conditional on’, ‘when’, ‘only when’, ‘in case’

Question 16

In ‘A->B’ which is the antecedent and which is the consequent of the conditional?

Answer 16

A is the antecedent and B is the consequent

Question 17

What is the truth table for ‘->’?

Answer 17

A¦ B¦ A->B ¦
T¦ T¦ T ¦
T¦ F¦ F ¦
F¦ T¦ T ¦
F¦ F¦ T ¦

Question 18

Give an example of a modus ponens argument using ‘if-then’

Answer 18

P1 A->B If Serena is muscular
then serena is strong
P2 A Serena is muscular
___________________ ________________________
C B Serena is strong

Question 19

Give an example of a modus tollens argument using ‘if-then’

Answer 19

P1 A->B If Daphne is a cat, then
Daphne meows
P2 ~B Daphne doesn’t meow
___________________ ________________________
C ~A Daphne is not a cat

Question 20

Give an example of a bad argument using ‘if-then’, denying the antecedent

Answer 20

P1 A->B If you smoke, you’re
likely to get heart
disease
P2 ~A I don’t smoke
___________________ ________________________
C ~B I’m not likely to get
heart disease

This conclusion could be false as the risk might be genetic.

Question 21

Give an example of a bad argument using ‘if-then’, affirming the consequent

Answer 21

P1 A->B If vaccination is
widespread infections
are down
P2 B Infections are down
___________________ ________________________
C A Vaccination is
widespread

This conclusion could be false as it could be the lockdown.

Question 22

What’s the correct truth table for ‘A if B’?

Answer 22

B->A

IM NOT SURE

Question 23

What’s the correct truth table for ‘A only if B’?

Answer 23

A->B
The second row shows this

IM NOT SURE

Question 24

What are some other ways of signalling the conclusion?

Answer 24

‘so’, ‘hence’, ‘thus’, ‘therefore’, ‘it follows that…’