Properties Flashcards
0
Q
Associative
A
Add:(a+b)+c=a+(b+c)
Multiply:(a•b)•c=a•(b•c)
1
Q
Commutative
A
Add: a+b=b+a
Multiply: ab=ba
2
Q
Distributive
A
Add:———-
Multiply:a(b+c)=ab+bc
3
Q
Identity
A
Add:a+0=a and 0+a=a
Multiply:a•1=a and 1•a=a
4
Q
Inverse
A
Add: a+(-a)=0
Multiply:a•(1/a)=1
5
Q
Equality
A
Add: If a=b, then a+c=b+c
Multiply: If a=b, then ac=bc
6
Q
Reflexive
A
a=a
7
Q
Symmetric
A
If a=b, then b=a
8
Q
Transitive
A
If a=b and b=c, then a=c
9
Q
Substitution
A
If a=b, then a can replace b in any mathematical statement
10
Q
Trichotomy
A
For any two real numbers a and b, exactly one of the following is true: a=b, a>b, or a<b
11
Q
Inequality addition
A
If a>b, then a+c>b+c
12
Q
Inequality multiplication
A
If a>b and c>0, then ac>bc
If a>b and c<bc
13
Q
Inequality transitive
A
If a>b and b>c, then a>c
