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Properties of Logical Operators
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¬
¬
a
=
a
¬
⊥
=
⊤
¬
⊤
=
⊥
a
∨
⊥
=
a
a
∧
⊤
=
a
a
∨
¬
a
=
⊤
a
∧
¬
a
=
⊥
Commutative laws
a
∨
b
=
b
∨
a
a
∧
b
=
b
∧
a
Associative laws
a
∨
b
∨
c
=
a
∨
b
∨
c
a
∧
b
∧
c
=
a
∧
b
∧
c
Distributive laws
a
∨
b
∧
c
=
a
∨
b
∧
a
∨
c
a
∧
b
∨
c
=
a
∧
b
∨
a
∧
c
Absorption laws
a
∨
a
∧
b
=
a
a
∧
a
∨
b
=
a
Idempotent laws
a
∨
a
=
a
a
∧
a
=
a
De Morgan's laws
¬
a
∨
b
=
¬
a
∧
¬
b
¬
a
∧
b
=
¬
a
∨
¬
b
Keywords: Properties of Logical Operators
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