Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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.