Axioms Flashcards
(15 cards)
1
Q
a+b is a real number
A
Closure for Addition
2
Q
ab is a real number
A
Closure for Multiplication
3
Q
a + b = b + a
A
Commutativity for Addition
4
Q
ab = ba
A
Commutativity for Multiplication
5
Q
a + (b + c) = (a + b) + c
A
Associativity for Addition
6
Q
a(bc) = (ab)c
A
Associativity for Multiplication
7
Q
c(a + b) = ca+ cb ; (a + b)c = ac+ bc
A
Distributivity of Multiplication over Addition
8
Q
a + 0 = a ; 0 + a = a
A
Additive Identity
9
Q
a ∙ 1 = a ; 1 ∙ a = a
A
Multiplicative Identity
10
Q
a + -a = 0 ; -a + a = 0
A
Additive Inverse
11
Q
a = a
A
Reflexive Property for Equality
12
Q
if a = b, then b = a
A
Symmetric Property for Equality
13
Q
if a = b and b = c, then a = c
A
Transitive Property for Equality
14
Q
if a = b, then a + c = b + c
A
Addition Property for Equality
15
Q
if a = b, then ac = bc
A
Multiplication Property for Equality
