With a domain from -2 to 2 I'm trying to write the following using disjunctions conjunctions and nagations. I'm not sure how correct I am and wanted to know if I did them correct? Could someone help with the last one I just cant figure out how to start that expression?
$∀ x\ P(x) = P(-2) ∧ P(-1) ∧ P(0) ∧ P(1) ∧ P(2)$
\neg ∀x\ P(x) = (P(−2)∨P(−1)∨P(0)∨P(1)∨P(2))∧¬(P(−2)∧P(−1)∧P(0)∧P(1)∧P(2))
In English doesn't that mean: At least one element is true and one element is false?∃x\ \neg P(x) = $
Edit: The last two with the correct answer of "At least one is not true".
∃x¬P(x) = ¬P(-2) ∨¬P(-1) ∨¬P(0) ∨¬P(1) ∨¬P(2)
¬∀xP(x) = ¬(P(-2) ∧ P(-1) ∧ P(0) ∧ P(1) ∧ P(2))