Proprietatile algebrei booleene
2
Proprietǎtile algebrei booleene idempotenta o a + a = a 0 + 0 = 0 1 + 1 = 1 o a a = a ∙ 0 0 = 0 ∙ 1 1 = 1 ∙ comutativitatea a + b = b + a a b = b a ∙ ∙ asociativitatea (a + b) + c = a + ( b + c ) = a + b + c (a b) c = a ( b c ) = a b c ∙ ∙ ∙ ∙ ∙ ∙ distributivitatea a ( b + c ) = a b + a c ∙ ∙ ∙ simetria a = b b = a → reflexivitatea a = a tranzitivitatea a = c → Teoremele lui De Morgan 1.
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Transcript of Proprietatile algebrei booleene
Proprietǎtile algebrei booleene
idempotentao a + a = a
0 + 0 = 01 + 1 = 1
o a ∙ a = a0 ∙ 0 = 01 ∙ 1 = 1
comutativitateaa + b = b + aa ∙ b = b ∙ a
asociativitatea(a + b) + c = a + ( b + c ) = a + b + c(a ∙ b) ∙ c = a ∙ ( b ∙ c ) = a ∙ b ∙ c
distributivitateaa ∙ ( b + c ) = a ∙ b + a ∙ c
simetriaa = b → b = a
reflexivitateaa = a
tranzitivitatea
→ a = c
Teoremele lui De Morgan
1.
2.
Teoreme de absorbtie :
1. + =
2. a
3. a + = a + b
4. a = a b
5. a + c + b c = a b + c
6. (a + b) ( + c) (b + c) = (a + b) ( + c)
Alte relatii
+ 0 =
+ 1 = 1
∙ 0 = 0
∙ 1 =
+ = 1
∙ = 0
=
