class 4

Question 1

What we obtain by formalization

Answer 1

– Simplify natural language
– Eliminate ambiguities
– Capture the logical form

Question 2

declarative sentences

Answer 2

Premises and conclusions in arguments, linguistic expressions that can be (said) true or false.

Question 3

basic sentential operators (to form a complex sentence)

Answer 3

• Negation: not…
• Conjunction: … and …
• Disjunction: … or …
• Conditional: if … then …
• Bi-conditional: … if and only if …

Question 4

and

Question 5

not

Answer 5

–|

Question 6

or

Answer 6

v

Question 7

if

Answer 7

–>

Question 8

if and only if, iff

Answer 8

<–>

Question 9

God exists if and only if the cat is not on the sofa

Answer 9

q <–> –| p

Question 10

God does not exist or the cat is not on the sofa

Answer 10

–| q v –| p

Question 11

If the Prime Minister is on trial, he resigns, or the government loses
any credibility. The Prime Minister is on trial, and he does not resign,
so the government loses any credibility

Answer 11

p –> (q v r), p ^ –| q |- r

Question 12

If Paul or Quinn go to the party, then Robert goes too

Answer 12

(p v q) –> r

Question 13

It is not the case that Robert and Paul go to
the party

Answer 13

–| (r ^ p)

Question 14

If Robert goes to the party, then if Paul goes then Quinn does not

Answer 14

r –> (p –> –| q)

Question 15

–|p is true iff

Answer 15

p is false

Question 16

p ^ q’ is true iff

Answer 16

both p and q are true

Question 17

p v q is true iff

Answer 17

p or q is true, at least one

Question 18

p | q is true iff

Answer 18

exclusive disjunction, at least p or q is true, but they cannot be both true

Question 19

p –> q is true iff

Answer 19

it is not the case that the first
(antecedent) is true and the second (consequent) is false
–|(p ^ –|q)

Question 20

p <–> q

Answer 20

p and q have the same truth value : both false or both true
(p –> q) ^ (q –> p)

Question 21

If Robert goes to the party, then if Paul goes, then Quinn does not

Answer 21

r –> (p –> –|q)

Question 22

Paul goes to the party, but Quinn does not

Answer 22

p ^ –|q

Question 23

Neither Robert nor Quinn go to the party

Answer 23

–|r ^ –| q

Question 24

Quinn goes to the party if Paul does not go

Answer 24

–|p –> q

Question 25

Robert goes to the party only if Paul does not

Answer 25

r --> --| p

Question 26

Paul goes to the party even if Quinn goes

Answer 26

p ^ q

Question 27

Although Robert goes to the party, Paul does not go

Answer 27

r ^ --| p

Question 28

Robert goes to the party provided that Paul goes

Answer 28

r --> p

Question 29

Quinn goes to the party unless Robert goes

Answer 29

q v r which means that --|q --> r

Question 30

Given that ‘p’ is true, ‘q’ is false, and ‘r’ is true, check the truth value p ^ q

Answer 30

False, because ‘q’ is false (in case of ‘^’ both must be true)

Question 31

Given that ‘p’ is true, ‘q’ is false, and ‘r’ is true, check the truth value p --> q

Answer 31

False, because the antecedent is true but the consequent false (in case of ‘→’ it is the only false case)

Question 32

Given that ‘p’ is true, ‘q’ is false, and ‘r’ is true, check the truth value --|p v --| q

Answer 32

True, because ‘q’ is false, so one of the two disjuncts, ‘--|q’, is true (in case of ‘v’ that one is true is enough)

Question 33

Given that ‘p’ is true, ‘q’ is false, and ‘r’ is true, check the truth value q --> (p ^ --| r)

Answer 33

True because both, antecedent and consequent, are false

Question 34

Given that ‘p’ is true, ‘q’ is false, and ‘r’ is true, check the truth value (--|q ^ r) <--> p

Answer 34

True, because the two sides of the bi-conditional have the same T value

Question 35

Given that ‘p’ is true, ‘q’ is false, and ‘r’ is true, check the truth value (--| v r) --> --|q

Answer 35

True because both, antecedent and consequent, are true

Question 36

Given that ‘p’ is true, ‘q’ is false, and ‘r’ is true, check the truth value q --> (--|p<--> (--|r --> --|q))

Answer 36

true because it is possible for the antecedent to be negative and the consequent to be positive