BITSAT 2021 Paper

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.