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.
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)
2 answers
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)
(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)