Below are two strategies for determining the truth value of a statement involving a positive number x and another statement P(x). (i) Find some x > 0 such that P(x) is true. (ii) Let x be the name for...

Below are two strategies for determining the truth value of a statement involving a positive number x and another statement P(x).

(i) Find some x > 0 such that P(x) is true.

(ii) Let x be the name for any number greater than 0 and show P(x) is true.

For each statement below, indicate which strategy is more appropriate.

(a) ∀ x > 0, P(x). 􀂜

(b) ∃ x > 0
 P(x).

(c) ∃ x > 0
 ~ P(x).

(d) ∀ x > 0, ~ P(x).