- #1
Mishada17
- 3
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Hi, I'm taking an intro logic class and though I'm comfortable with most propositional logic, predicate logic is confusing me. I joined the forum to ask this particular question that I've been stuck on for a while. Any help would be appreciated - I'm having trouble finding information on the web since my teacher uses a different format that most of what I've seen elsewhere.
∃x F(x) |− ~(∀x ~F(x))
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
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. :'(
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. :'(