Règles de l'algèbre de Boole

Question 1

A quelle opération mathématique est associé AND ?

Answer 1

A la multiplication

Question 2

A quelle opération mathématique est associé OR ?

Answer 2

A l’addition

Question 3

Valeur nulle (version AND)

Answer 3

0 * x = 0

Question 4

Valeur nulle (version OR)

Answer 4

1 + x = 1

Question 5

Valeur neutre (version AND)

Answer 5

1 * x = x

Question 6

Valeur neutre (version OR)

Answer 6

0 + x = x

Question 7

Complément (version AND)

Answer 7

x * !x = 0

Question 8

Complément (version OR)

Answer 8

x + !x = 1

Question 9

Commutativité (version AND)

Answer 9

xy = yx

Question 10

Commutativité (version OR)

Answer 10

x + y = y + x

Question 11

Associativité (version AND)

Answer 11

x * (yz) = (xy)*z

Question 12

Associativité (version OR)

Answer 12

x + (y +z) = (x + y) + z

Question 13

Distributivité (version AND)

Answer 13

x * (y + z) = xy + xz

Question 14

Distributivité (version OR)

Answer 14

x + (yz) = (x+y)(x+z)

Question 15

Idempotence (version AND)

Answer 15

x * x = x

Question 16

Idempotence (version OR)

Answer 16

x + x = x

Question 17

Absorption (version AND)

Answer 17

x*(x+y) = x

Question 18

Absorption (version OR)

Answer 18

x + (x*y) = x

Question 19

Théorème de De Morgan (version AND)

Answer 19

!(x*y) = !x + !y

Question 20

Théorème de De Morgan (version OR)

Answer 20

!(x+y) = !x * !y