Cours d`introduction à la logique

−
π > 3
7 + 4 = 12
P Q R
P P
P P
P P
P Q P Q
P Q P Q
P Q
P Q P Q P Q

P Q P Q
P Q P Q
x > 3y < 2x≤3y≥2
P Q R P Q P R
P Q R P Q P R
P⇒Q P Q P Q
P Q
P⇔Q P Q P Q
P Q
P Q P ⇒Q P ⇔Q
P⇒Q P Q
3>4⇒2<−1 3 >4 2 <−1
P⇒Q P
Q P P Q
−P⇒Q
Q P Q
P−Q⇒P
f:R→RP f Q f P
Q Q
P
P⇔Q P ⇒Q Q ⇒P
P⇒Q Q ⇒P
P⇒Q P
Q⇒P P ⇒Q
n
n2⇒n ,
n⇒n2.
n k n = 2k+ 1
n2= (2k+ 1)2= 2(2k2+ 2k)+1 n2= 2k0+ 1 k0= 2k2+ 2k n2

∀∃
∀n∈N, n ≥3
∃n∈N, n ≥3n
EP P(x)x
EP
∀x∈EP(x)∃x∈EP(x)
∃x∈EP(x)∀x∈EP(x)
∀
∃ ∃ ∀
∃
∀
∃n∈N,∀m∈N, m ≤n,
∀m∈N,∃n∈N, m ≤n,
∀m∈N, m ≤n n
∃n∈N, m ≤n p n
m
∀
∃
∀x, ∀y, P(x, y)∀y, ∀x, P(x, y).
∀(x, y),P(x, y).
∃x, ∃y, P(x, y)∃y, ∃x, P(x, y).
∃(x, y),P(x, y).
∃!
∃!x∈R+, x2= 2 x x =√2