Suppose P, Q and R are distinct integers. R is a positive even integer, while P and Q are positive odd integers. Which one of the following expressions cannot be true?

Suppose P, Q and R are distinct integers. R is a positive even integer, while P and Q are positive odd integers. Which one of the following expressions cannot be true? Correct Answer (P - R)² is even.

Given:

P, Q and R are distinct integers.

R is positive even integer.

P and Q are positive odd integer.

Calculation:

Let, P = 1, Q = 3 and R = 2

From option (1)

Q(P - R) is odd.

⇒ Q( P - R) = 3 × (1 - 2)

⇒ -3 (odd)

From the above result, we can say that expression Q(P - R) is true.

From option (2),

(P - R)2 is even.

⇒ (P - R)² = (1 - 2)²

⇒ 1 (odd)

From the above result, we can say that ecpression (P - R)² cannot be true.

∴ The expression (P - R)2 cannot be true.