relations and properties (100%)

transitive

Of the three properties, reflexive, symmetric, and transitive that define the relation "is equal to," which one could also apply to "is less than" and "is greater than?"

Reflexive

5) The ___ Property of Equality states that for any number a,a=a.

additive

The ___ Identify Element defines 0 as such that a+0=0+a=a for all real numbers.

Commutative

The ___ Property of Addition states that for any numbers a and b,a+b=b+a .

inverse

The Additive ___ Property states that for every number a, there is a number -a, such that a+(-a)=(-a)+a=0.

Symmetric

The ___ Property of Equality states that for any numbers a and b, if a=b, then b=a.

Distributive

The ___ Property of Multiplication over Addition states that for any numbers a,b, and c,a⋅(b+c)=(a⋅b)+(a⋅c).

Associative

Property of Addition states that for any a, b, and c,a+(b+c)=(a+b)+c.

Multiplicative

The ___ Identity Property defines 1 as the multiplicative identity element because for every number a,a⋅1=1⋅a=a.

Multiplicative

The ___ Inverse Property states that for every number a except 0, there is a number a-1=1a such that a⋅(a-1)=(a-1)⋅a=1.

Transitive

The ___ Property of Equality states that for any numbers a,b, and c, if a=b and b=c, then a=c.

Commutative

The ___ Property of Multiplication states that for any numbers a and b,a⋅b=b⋅a.

Associative

The ___ Property of Multiplication states that for any numbers a,b, and c,a⋅(b⋅c)=(a⋅b)⋅c.

Trichotomy

The ___ Property states that for any numbers a and b, either a<b,a=b, or a>b.