BITSAT Mathematics Question (2021) — Solution

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.