Question

Suppose that the domain of discourse is the set {-2, -1, 0, 1, 2}. Express the following statements without using quantifiers, using only the connectives ¬, V, Λ.

(a) ∃x P(x)
(b) ∀x P(x)
(c) ∃ ¬P(x)
(d) ∀ ¬P(x)
(e) ¬∃ P(x)
(f) ¬∀ P(x)

Answer 1

I have seen your post several times. Have not answered it since I am not familiar with the topic.

The last time I would have seen something like that must be about 55 years ago and it has long since gone into my "delete" part of my memory.

Answer 2

As I recall,

(a) ∃x P(x)
means "there exists an x such that P)x) is true. So, in this case, that wold be

P(-2) V P(-1) V P(0) V P(1) V P(2)

Hmmm. Not sure what (c) ∃ ¬P(x) means. There exists "not P(x)"?

Is that the same as

∃x ¬P(x), that is

there exist x such that P(x) is false

??

In any case, it appears that you just have to replace P(x) with suitable connections of P(-2)...P(2)