Q75,paper 3, D 12. Let Q(x, y, z) be the statement “x + y = z” and let there be two quantifications given as

(i) vx vy ƎZ q(x, y, z)

(ii) ƎZvxvyq(x, y, z)  Where x, y, z are real numbers. Then which one of the following is correct ?

(A) (i) is true and (ii) is true.

(B) (i) is true and (ii) is false.

(C) (i) is false and (ii) is true.

(D) (i) is false and (ii) is false

Answer(B).
For every x,y there exists a unique Z.
For(1,1), z is 2
For(1,2) z is 3.
For(2,1) z is 3. Hence option 1 is true.
Statement 2 can be refuted as there cannot be a single answer for all the combination of x,y.