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Question

Let θ(x, y, z) be the statement “x + y = z” and let there be two quantifications given as

(i) ∀x ∀y  Z ∃ θ(x, y, z)
(ii) ∃Z ∀x ∀y θ(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).(i) is true and (ii) is false

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Q. Let θ(x, y, z) be the statement “x + y = z” and let there be two quantifications given as (i) ∀x ∀y  Z ∃ θ(x, y, z) (ii) ∃Z ∀x ∀y θ(x, y, z)   Where x, y, z are real numbers....

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