Which property can be used to deduce a = b, b = c, therefore a = c?

Which property can be used to deduce a = b, b = c, therefore a = c?

• A. Transitive Property
• B. Addition Property
• C. Symmetric Property
• D. Reflexive Property

Answer: (A)

The main idea tested is the transitive property of equality: if a = b and b = c, then a = c. This rule lets you connect two equalities to conclude the third relation directly, which is exactly what you need here. You’re given a = b and b = c, so by transitivity you can deduce a = c. The other properties don’t directly give that conclusion. The addition property would require adding the same value to both sides of an equation to preserve equality, not deducing a consequence from two separate equalities. The symmetric property says that if a = b then b = a, which is useful for flipping the order but doesn’t combine two equalities into a new one. The reflexive property says every element is equal to itself, a = a, which doesn’t connect different symbols like a, b, and c. So the transitive property is the one that yields a = c from a = b and b = c.

The main idea tested is the transitive property of equality: if a = b and b = c, then a = c. This rule lets you connect two equalities to conclude the third relation directly, which is exactly what you need here. You’re given a = b and b = c, so by transitivity you can deduce a = c.

The other properties don’t directly give that conclusion. The addition property would require adding the same value to both sides of an equation to preserve equality, not deducing a consequence from two separate equalities. The symmetric property says that if a = b then b = a, which is useful for flipping the order but doesn’t combine two equalities into a new one. The reflexive property says every element is equal to itself, a = a, which doesn’t connect different symbols like a, b, and c.

So the transitive property is the one that yields a = c from a = b and b = c.