Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 Help Me ! » Quantifiers and a predicate » 2013-04-04 15:21:35

FlashBurn
Replies: 2

I'm trying to understand what happens when quantifiers in the prediate are swapped.

Let's assume the following:
Two sets A and a D and a predicate H(a, d), where a ∈ A and d ∈ D.

Statement 1.

There exists d ∈ D for all a ∈ A such that H(a, d).

This one I can figure out. It means that there exists a single d for all a such that H(a, d).

Statement 2.

For all a ∈ A there exists d ∈ D such that H(a, d).

This one I can't figure out. Does it mean that for every a there exists a unique d, i.e a1 - d1, a2 - d2, a3 - d3 etc. or does it mean that d's can be shared by some a's, i.e. a1 - d1, a2 - d2, a3 - d1, a4 - d2  etc.

Any help is appreciated.

Board footer

Powered by FluxBB