Quelques concepts et notations logico-mathématiques

∧
→
↔
¬
∀
∃
∈
/∈
⊆
∅
{x∈X:...}x X
∪
∪i∈Ii
∩
∩i∈Ii
(x, y)x y
A×B
f:A→B A B
N
Pn
i=0 aia0an
Pn
i=0 ai=a0+... +an
Qn
i=0 aia0an
Qn
i=0 ai=a0×... ×an
R

ab
a b
ab
a b
∧
(ab)∧(bc)
a b b c
→
(ab∧bc)→ac
a b b c a c

φ ψ φ ψ
φ
ψ
↔
(b∼c)→(ab↔ac)
b c a b a c
φ ψ
φ ψ
φ ψ φ ψ ψ φ
φ ψ
ψ φ
¬
(ab)→ ¬(ba)
a b b a
∀

a
x a x
∀x a x
∃
a
x x a
∃x x a
A
C
{...}A={...}A
N
∈

1∈N
/∈
a /∈X
a X
∅
A
•A={0,1,2,3,4}
•A
|
A={x∈N:x≤4}
A B A
B x x ∈A x ∈B
⊆ 6⊆
• {1,2,4}⊆{1,2,3,4}
• {1,2,3,4}⊆{1,2,3,4}
• {4,5} 6⊆ {1,2,3,4}