Certainly! I'll identify the property described by each given equation. Let's go through them step-by-step:
1. [tex]\(a + b = b + a\)[/tex]
This equation states that when two numbers are added, the order in which they are added does not affect the sum. This property is known as the Commutative property of addition.
2. [tex]\(a(b + c) = ab + ac\)[/tex]
This equation shows that a single term multiplied by a sum of two terms is equal to the sum of the single term multiplied by each of those two terms individually. This property is known as the Distributive property.
3. [tex]\(a(bc) = (ab)c\)[/tex]
This equation indicates that when multiplying three terms, the grouping of which two terms are multiplied first does not affect the product. This property is known as the Associative property of multiplication.
4. If [tex]\(a = t\)[/tex] and [tex]\(a + b = c\)[/tex], then [tex]\(t + b = c\)[/tex]
This equation reflects the idea that if two expressions are equal, then one of the expressions can be substituted for the other in any equation. This property is known as the Substitution property.
5. For all [tex]\(a\)[/tex] and [tex]\(b\)[/tex], [tex]\(a > b\)[/tex] or [tex]\(a < b\)[/tex] or [tex]\(a = b\)[/tex]
This equation states that for any two real numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex], one of them must be greater than, less than, or equal to the other. This property is known as the Trichotomy property.
To summarize, the properties described by each equation are:
1. Commutative property of addition
2. Distributive property
3. Associative property of multiplication
4. Substitution property
5. Trichotomy property
