The statement p: For any real numbers x, y if x=y , then 2 x+a=2 y+a when a Z .

Step-by-step solution

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