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What property would justify the following statement?

If [tex]a = b[/tex] and [tex]b = c[/tex], then [tex]a = c[/tex].

A. Addition Property
B. Reflexive Property
C. Subtraction Property
D. Transitive Property

Sagot :

To understand which property justifies the statement "If [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]," we need to consider the different properties of equality in mathematics.

1. Addition Property: This property states that if [tex]\(a = b\)[/tex], then [tex]\(a + c = b + c\)[/tex] for any [tex]\(c\)[/tex]. This property is related to the addition of equal quantities.

2. Reflexive Property: This property states that any quantity is equal to itself, i.e., [tex]\(a = a\)[/tex]. It is fundamental but does not involve multiple quantities or the chaining of equalities.

3. Subtraction Property: This property states that if [tex]\(a = b\)[/tex], then [tex]\(a - c = b - c\)[/tex] for any [tex]\(c\)[/tex]. This property is similar to the addition property but involves subtraction.

4. Transitive Property: This property states that if [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]. It involves three quantities and shows how the equality can be transferred across them.

The given statement "If [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]" is directly described by the Transitive Property. This property allows us to conclude that two things are equal if they are both equal to a third thing.

Given the options, the property that would justify the statement is:
- Transitive Property

Therefore, the correct answer is the 4th option: Transitive Property.