Let us assume x = 5 and y = 3 are two odd numbers and z = 2 is and even number. Case I: (x−z)2y=(5−2)2×3=9×3=27 is odd. Case II: (x−z)2y2=(5−2)2×32=9×9=81 is odd. Case III : (x−z)y=(5−2)×3=9 is odd. Case IV: (x−y)2x=(5−3)2×2=4×2=8 is even. Only the option (a) (x−z)2y is even, cannot be true.