- #1

- 3

- 0

## Homework Statement

∃x F(x) |− ~(∀x ~F(x))

## Homework Equations

Lecture information may be found on these two pages:

http://people.cis.ksu.edu/~schmidt/301s11/Lectures/5natdedS.html

http://people.cis.ksu.edu/~schmidt/301s11/Lectures/6quantS.html

## The Attempt at a Solution

1. ∃x F(x) premise

-----------------

2. a ∀x ~F(x) assumption - I think this is the right assumption because I want to ~it, right?

3. ~ F(a) ∀e 2

4. ∃a ~F(a) ∃i 3

-----------------

5. ∃x ~F(x) ∃e 1 2-4

... beyond here I have no idea. I think I need to find an _|_ but so far the closest I've come is ∃x~F(x) and ∃x F(x) and those apparently don't contradict because ~e won't work on them. :'(