1° Let
p: He needs a doctor
q: He needs a lawyer
r: He has an accident
s: He is sick
u: He is injured
Then, translate the following formulas to English
A: (s → p) ^ (r → q)
B: (p ^ q) ↔ (s ^ u)
C: ~ (s v u) → ~ p
2° If the congress refuses to enact new laws, then the strike will not end up, or it lasts more than one year and the president resigns. Suppose the congress defuses to act, the strike is over, and the president does no resign.
Has the strike lasted more than one year?
First question:
A: If he is sick then he needs a doctor and he had an accident then he needs a lawyer.
B: He needs a doctor and a lawyer only if he is sick and he is injured.
C: He is not ill or is injured then he does not need a doctor.
Second question:
b = F
d = F
c = ?
F1 ^ F2 ^ F3 ^ F4 → G
Propositions:
a: If the congress refuses to enact new laws.
b: Then the strike will not end up.
c: The strike last more than one year.
d: The president resigns.
a = V b: Then the strike will not end up.
c: The strike last more than one year.
d: The president resigns.
b = F
d = F
c = ?
F1: a → b v c ^ d
F2: a
F3: ~ b
F4: ~d
F2: a
F3: ~ b
F4: ~d
F1 ^ F2 ^ F3 ^ F4 → G
Tautology
So G is true.
Conclusion: The strike lasted more than a year.
Conclusion: The strike lasted more than a year.
