class 5

Question 1

p v q’ is true in three possible worlds

Answer 1

p + q
not p + q
p + not q
The only excluded world is not p + not q

Question 2

p → q is true in three worlds

Answer 2

p + q
not p + q
not p + not q
The only excluded world is p + not q

Question 3

DISJUNCTIVE SYLLOGISM explanation

Answer 3

Premise 1 = ‘Juliette is blonde or longhaired’
Three possibilities/worlds:
* A. blonde + longhaired
* B. blonde + not longhaired
* C. not blonde + longhaired
Premise 2 = ‘Juliette is not longhaired’
We know we are in the world B:
Conclusion = Juliette is blonde

Question 4

DISJUNCTIVE SYLLOGISM formula

Answer 4

p v q , –|p |-q

Question 5

MODUS PONENS explanation

Answer 5

Premise 1 = ‘If you drink so much you have an accident’
* A. drink + accident
* B. not drink + accident
* C. not drink + not accident
Premise 2 = ‘you drank a lot’
* The only possible case is the world A
* Conclusion = You have an accident

Question 6

MODUS PONENS formula

Answer 6

p –> q, p|- q

Question 7

MODUS TOLLENS formula

Answer 7

p –> q, –|q |- –|p

Question 8

MODUS TOLLENS explanation

Answer 8

1. If Juliette is German, then she’s European
   * A. German + European
   * B. not German + European
   * C. not German + not European
2. Juliette is not European
   The only possible world is C:
   Conclusion: Juliette is not German

Question 9

Hypothetic syllogism formula

Answer 9

p –> q, q –> r |- p –> r

Question 10

Negation of →

Answer 10

–| p –> q |- p ^ –| q

Question 11

De Morgan laws (DeM) 1 explanation

Answer 11

“It is not true that I killed my wife and put the corpse in the fridge” =
I did not kill my wife or I did not put the corpse in the fridge

Question 12

De Morgan laws (DeM) 1 formula

Answer 12

–| (p ^ q) |- –|p v –|q

Question 13

De Morgan laws (DeM) 2 explanation

Answer 13

“It is not true that I killed my wife or put the corpse in the fridge” =
I did no kill my wife and I did not put the corpse in the fridge

Question 14

De Morgan laws (DeM) 2 formula

Answer 14

–| (p v q) |- –|p ^ –|q

Question 15

Constructive dilemma:
You resist temptations, or you don’t resist
If you resist, you are unhappy, because you don’t satisfy your wishes
if you do not resist, you’re unhappy, because you ruin yourself
So in any case you are unhappy

Answer 15

p v q, p –> r, q –> r |- r
in any case of this dichotomy, the result is r

Question 15

general DeM

Answer 15

v becomes ^ and vice versa, extend the negation to both terms