Which statement is an example of the symmetric property of equality?

Which statement is an example of the symmetric property of equality?

• A. If a = b, then b = a
• B. If a = b, then a ≠ b
• C. If a = b, then a = b
• D. If a = b, then b = c

Answer: (A)

The symmetric property of equality says you can swap the two sides of an equation without changing truth: if a = b, then b = a. The statement that demonstrates this directly is exactly that reversal, showing equality holds when the sides are flipped. The other options fail for different reasons: one asserts that a = b implies a ≠ b, which contradicts the premise; another says a = b implies a = b, which is true but reflects the reflexive property, not the idea of swapping sides; and the last introduces a different variable, suggesting b = c, which is unrelated to what follows from a = b. So the statement that exactly captures the symmetric idea is the reversal of the sides.

The symmetric property of equality says you can swap the two sides of an equation without changing truth: if a = b, then b = a. The statement that demonstrates this directly is exactly that reversal, showing equality holds when the sides are flipped.

The other options fail for different reasons: one asserts that a = b implies a ≠ b, which contradicts the premise; another says a = b implies a = b, which is true but reflects the reflexive property, not the idea of swapping sides; and the last introduces a different variable, suggesting b = c, which is unrelated to what follows from a = b.

So the statement that exactly captures the symmetric idea is the reversal of the sides.