We prove the statement p is true by contrapositive method and by direct method. Direct method: For any real number x and y, x = y ⇒ 2x = 2y ⇒ 2x + a = 2y + a a for some a ∈ Z Contrapositive method: The contrapositive statement of p is "For any real numbers x,y if 2x + a ≠2y + a, where a ∈ Z , then x ≠y." Given , 2x + a ≠2y + a ⇒ 2x ≠2y ⇒ x ≠y Hence, the given statement is true.