Formal Logic Laws Flashcards
Commutative Law
a ^ b = b ^ a
Associative Law
a ^ (b ^ c) = (a ^ b) ^ c
Distributive Law
a ^ (b V c) c) = (a ^ b) V (a ^ c)
Double Negation Law
~~a = a
Identity Law
a ^ True = a | a V False = a
Negation Law
a ^ ~a = False a V ~a = True
Universal Bound Law
a ^ False = False | a V True = True
Negation of Universal Law
~True = False | ~False = True
Idempotent Law
a ^ a = a | a V a = a
De Morgan’s Law
~(p ^ q) = ~p V ~q
Absorption Law
a ^ (a V b) = a | a V (a ^ b) = a
Conditional Identities
p -> q = ~p V q | p q = q -> q ^ p -> q
Commutative Axiom
a * b = b * a
Associativity Axiom
a * b * c = (a * b) * c
Distributivity Axiom
a * (b + c) = a * b + a * c
Identity Elements Axiom
0 + x = x | 1 * x = x
Additive Inverse Axiom
x + i = y then x = y + -i
Trichotomy of and = Axiom
∀(x, y) [(x > y) v (x < y) v (x = y)]
Transitivity of < and > Axiom
∀(x, y) [(x > y ^ y > z) -> (x > z)]
Addition of integers preserve inequality Axiom
∀(x, y, z) [(x > y) -> (x + a > y + a)]
Multiplication of integers preserve inequality Axiom
∀(x, y, z) [(x > y) -> (x * a > y * a)]
Reflectivity Axiom
a = a
Transitivity Axiom
a = b, b = c then a = c
Symmetry Axiom
a = b iff b = a
Axioms of Closure
The sum, difference, and product of any two integers is an integer
Integer Axiom
No integer between 0 and 1
