The following is an indirect proof of the Addition Property of Equality: For real numbers a, b, and c, if a = b, then a + c = b + c. Assume____________. According to the given information, a = b. By the Subtraction Property of Equality, one can subtract the same number from both sides of an equation without changing the equation. Therefore, a + c − c ≠ b + c − c. Through subtraction, the c's cancel and a ≠ b. This contradicts the given information so a + c = b + c. Which statement accurately completes the proof?

Question

The following is an indirect proof of the Addition Property of Equality: For real numbers a, b, and c, if a = b, then a + c = b + c.  Assume____________. According to the given information, a = b. By the Subtraction Property of Equality, one can subtract the same number from both sides of an equation without changing the equation. Therefore, a + c − c ≠ b + c − c. Through subtraction, the c's cancel and a ≠ b. This contradicts the given information so a + c = b + c.  Which statement accurately completes the proof?