Anonymous asked in Science & MathematicsMathematics · 2 months ago

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

  • cosmo
    Lv 7
    2 months ago
    Favorite 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.

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