# Finding truth value of a statement?

The problem reads:

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

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

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

Which of these two strategies is appropriate for finding the truth value of the statement ∃x > 0 ϶ ∼ P(x)?"

I've been stuck on this for a while now, I just don't see how the two strategies differ. Any help is appreciated.

### 1 Answer

- cosmoLv 71 month agoFavourite answer
The "statement" says that "not P" is true for all x. So if you can find any single x which makes P true, then the "statement" is false. That's the first strategy.

Now, if the "statement" is in fact actually true, to prove it's true will require the second strategy, possibly a proof by induction.