Correction des exemples

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A1=
A2=
A3=
N
N=card(A1∪A2∪A3)
N=card(A1) + card(A2) + card(A3)
−card(A1∩A2)−card(A1∩A3)−card(A2∩A3)
+card(A1∩A2∩A3)
N= 35 + 20 + 5 −10 −3−1+1

E1
2 3
Card(E) = 32 ×31 ×30
A
1er
2eme 3eme
Card(A) = 24 ×23 ×22
B
A E
Card(B) = Card(CEA)
=Card(E)−Card(A)
= 32 ×31 ×30 −24 ×23 ×22
= 17616
A
Card(A) = 3
B
Card(B) = 2

Card(A×B) = Card(A)×Card(B) = 6
Ai=i
Card(A1∪A2∪A3) = Card(A1) + Card(A2) + Card(A3)
−Card(A1∩A2)−Card(A1∩A3)−Card(A2∩A3)
+Card(A1∩A2∩A3)
Card(Ai)
∀i Card(Ai) = 24= 16
Card(Ai∩Aj) :
∀(i, j), i 6=j Card(Ai∩Aj) = 14= 1
Card(A1∩A2∩A3) :
Card(A1∩A2∩A3) = 04= 0
Card(A1∪A2∪A3) = 16 + 16 + 16 −1−1−1 + 0 = 45
E
Card(E) = 34= 81
B A1∪A2∪A3
E
Card(B) = Card(E)−Card(A1∪A2∪A3) = 81 −45 = 36