Memento 1/6 - Ensembles, relations, graphes.

n x ≤y
¬ ∨
∧ ⇒ ⇔
F G
F≡G
A⇒B¬A∨B
¬B⇒ ¬A A ⇔B
(A⇒B)∧(B⇒A)
¬(A∨B)≡(¬A∧ ¬B)¬(A∧B)≡(¬A∨ ¬B)
A B ¬A A ∨B A ∧B A ⇒B A ⇔B
F F V F F V V
F V V V F V F
V F F V F F F
V V F V V V V
N
∃ ∀ =
∈
N
A B A =B⇔(A⊆B)∧(B⊆A)
E P (x)
{x∈E|P(x)}
E P (x)
EP(E)
EP({a, b}) = {∅,{a},{b},{a, b}} (a, b) :=
{{a},{a, b}} a b {a, b}
(a, b) = (c, d)⇔(a=c)∧(b=d)
(a, b)a∈E b ∈F E ×F
E F
E R
x y E
x R y R(x, y) (x, y)R
R{(x, y)∈E×E|x R y}
E
∀x∈E, x R x ∀(x, y)∈E×E, x R y ⇒y R x
∀(x, y, z)∈E3(x R y)∧(y R z)⇒x R z
x y
∀(x, y)∈E×E, (x R y)∧(y R x)⇒(x=y)
x
x y (x, y)x R y
a
b
c a
b
a
b
c
a
b
c
d
c
a b b a
c→a→b→c c
E R x y
1x R y 0
a b c d
a0 1 0 1
b0 1 0 1
c0101
d0 0 0 0
1
(x, y, z)x→y y →z(c, b, d)
1