The given property of equality can be described as follows: "For any numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex], if [tex]\(a = b\)[/tex], then [tex]\(b = a\)[/tex]."
Let's analyze each possible answer choice to determine which best describes this property:
1. Symmetric Property of Equality:
- This property states that if [tex]\(a = b\)[/tex], then [tex]\(b = a\)[/tex]. It emphasizes that the relationship works both ways: if [tex]\(a\)[/tex] is equal to [tex]\(b\)[/tex], then [tex]\(b\)[/tex] must also be equal to [tex]\(a\)[/tex]. This directly matches the given property in the question.
2. Associative Property:
- The Associative Property is related to how numbers are grouped in addition or multiplication, not to equality. For example, [tex]\((a + b) + c = a + (b + c)\)[/tex] or [tex]\((a \cdot b) \cdot c = a \cdot (b \cdot c)\)[/tex]. This property does not pertain to [tex]\(a = b\)[/tex] and [tex]\(b = a\)[/tex].
3. Reflexive Property:
- The Reflexive Property states that any number is equal to itself, i.e., [tex]\(a = a\)[/tex]. This means that each number is inherently equal to itself, which is not the situation described by the given property.
4. Transitive Property:
- The Transitive Property states that if [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]. This property deals with a chain of equalities, but it does not address the direct reversal of [tex]\(a = b\)[/tex] to [tex]\(b = a\)[/tex].
Given this analysis, the property in question is the Symmetric Property of Equality, since it specifically describes the mutual relationship where if [tex]\(a = b\)[/tex], then automatically [tex]\(b = a\)[/tex].
Therefore, the correct answer is:
Symmetric
