Question

1. consider the following argument. given: ( ab = 17 ) conclusion: ( ab - 2 = 15 ) which of the following properties does this illustrate? a the multiplication property of equality. b the subtraction property of equality. c the transitive property of equality. d the symmetric property of equality. e the reflexive property of equality.

Explanation:

To determine the property, we analyze each option:

• Option A: Multiplication property involves multiplying both sides, not subtraction. Eliminate.
• Option B: Subtraction property of equality states that if \( a = b \), then \( a - c = b - c \). Here, \( AB = 17 \), so \( AB - 2 = 17 - 2 = 15 \), which matches this property.
• Option C: Transitive property is \( a = b \) and \( b = c \) implies \( a = c \), not applicable here. Eliminate.
• Option D: Symmetric property is \( a = b \) implies \( b = a \), not applicable. Eliminate.
• Option E: Reflexive property is \( a = a \), not applicable. Eliminate.

Answer:

B. The subtraction property of equality.