Adv Algebra 1 Proofs And Axioms Flashcards
1
Q
Commutative Axiom
A
a+b=b+a
ab=ba
2
Q
Associative Axiom
A
(a+b)+c=a+(b+c)
(ab)c=a(bc)
3
Q
Distributive Axiom
A
a(b+c)=ab+ac
4
Q
Axioms of Equality
A
Reflexive Axiom
Symmetric Axiom
Transitive Axiom
5
Q
Reflexive Axiom
A
a=a
6
Q
Symmetric Axiom
A
If a=b then b=a
7
Q
Transitive Axiom
A
If a=b and b=c then a=c
8
Q
Cancellation Property of Opposites
A
-(-a)=a
9
Q
Identity Axiom of Addition
A
a+0=a
10
Q
Axiom of Additive Inverses
A
a+(-a)=0
11
Q
Property of the Opposites of a Sum
A
-(a+b)=-a+(-b)
12
Q
Definition of Subtraction
A
a-b=a+(-b)
13
Q
Identity Axiom of Multiplication
A
a(1)=a
14
Q
Multiplicative Property of Zero
A
a(0)=0
15
Q
Property of Opposites in Products
A
(-a)(b)=-ab
a(-b)=-ab
(-a)(-b)=ab
16
Q
Multiplication Property of -1
A
a(-1)=-a
17
Q
Property of Reciprocal of Product
A
1/a (1/b)=1/ab
18
Q
Axiom of multiplicative inverse
A
a(1/a)=1
