Boolean Algebra Flashcards
[Boolean Identities]
What is Double Negation?
¬(¬ x )
¬(¬ x ) = x
[Boolean Identities]
What is Idempotent Law?
x + x
x * x
x + x = x
x * x = x
[Boolean Identities]
What is Idempotent Law?
x + 0
x * 1
x + 0 = x
x * 1 = x
[Boolean Identities]
What is Domination Law?
x + 1
x * 0
x + 1 = 1
x * 0 = 0
[Boolean Identities]
What is Computative Law?
x + y
x * y
x + y = y + x
x * y = y * x
[Boolean Identities]
What is Associative Law?
x+(y+z)
x(yz)
x+(y+z) = (x+y) + z
x(yz) = (xy)z
[Boolean Identities]
What is Distributive Law?
x + (y*z)
x * (y+z)
x + (yz) = (x+y) * (x+z)
x * (y+z) = (xy) + (x*z)
[Boolean Identities]
What is Absorption Law?
x + xy
x (x+y)
x + xy = x
x (x+y) = x
[Boolean Identities]
What is De Morgan’s Law?
(x*y)^1
(x+y)^1
*^1 is complement
(x*y)^1 = x̄ + ȳ
(x+y)^1 = x̄ * ȳ
[Boolean Identities]
What is Complement Law?
x + x̄
x * x̄
x + x̄ = 1
x * x̄ = 0
[Boolean Identities]
What is Inversion?
0^1
1^1
where ^1 is complement
0^1 = 1
1^1 = 0
[Boolean Symbols]
What does ‘ + ‘ means in English and in Set Theory?
English : OR
Set Theory: Union (∪)
Logical Connections: Conjunction
(∧)
[Boolean Symbols]
What does ‘ * ‘ means in English and in Set Theory?
English : AND
Set Theory: Intersect (∩)
Logical Connections: Disjunction
(∨)
[Boolean Symbols]
What does ‘ x̄ ‘ means in English and in Set Theory?
English : NOT
Set Theory: p^1
Logical Connections: Negate (¬)
[Boolean Symbols]
What does ‘ 1 ‘ means in English and in Set Theory?
English : Universe
Set Theory: u
Logical Connections: True
