Q 17,paper 3,J 12. Let Q(x, y) denote “x+ y = 0” and let there be two quantifications given as

Options
(i) ∃y∀x Q(x, y)
(ii) ∀x∃y Q(x, y) where x& y are real numbers. Then which of the following is valid ?
(A) (i) is true & (ii) is false.
(B) (i) is false & (ii) is true.
(C) (i) is false & (ii) is also false.
(D) both (i) & (ii) are true.
Answer(B) (i) is false & (ii) is true.
Explanation. The universe of discourse is the set of all things we wish to talk about; that is, the set of all objects that we can sensibly assign to a variable in a propositional function. Let us consider that ∃y∀x Q(x, y) There exists a y for every x equation x+y=0. Let x=1 then y should be -1. Let x=2 then y should be -2. So it is different for every value of X. So it is for every x there exists a y where x+y=0. So premises 2 is right.