Feuille d`exercices n◦

◦2
x y
x∧y x ∨y xc{x,y}
x
F⊆EP(F)P(E)
A= (A, ∧,∨,c,0,1) B A
B= (B, ∧,∨,c,0,1) A
0 1 ∧ ∨
B∧c
B s : (x,y)7→ (xc∧yc)
A= (A, 6)≤A
p∈A B ={x∈A;x6p} B = (B, 6)
Ah:x7→ x∧p
A B
Aa A
∀x∈A(x≤a→(x= 0 x=a)).
A
a6= 0 A
∀x∈A(a≤x a ≤xc);
∀x,y ∈A(a≤x∨y→(a≤x a ≤y)).
AS ϕ
A P(S)
ϕ:A −→ P(S)
x−→ {a∈S;a≤x}
P(S)S
A A
P LP
P
P

P P ={p1, . . . ,pn}
LP
S={α1∧. . . ∧αn; 1 ≤i≤n αi=piαi=¬pi}
P(S)
Aφ A A
{x∈A , φ(x)≤x} {x∈A , φ(x)≥x}φ
x∈A φ(x) = x
EA P(E)
a∈Eˆa=T
x∈A,a∈x
x x ∈A x =S
a∈x
ˆa b ∈E
b∈ˆa a ∈ˆ bˆ b= ˆa
M⊆A(T
x∈M
x)∈AAS={ˆa|a∈E}
A A P(S)S
AF A F 0
F0={xc;x∈F}
FAF∪F0A
EP(E)P(F)F(E E