1. The problem asks to express the proposition \(\exists x P(x)\) where the domain of \(x\) is \{-2, -1, 0, 1, 2\} using only disjunctions, conjunctions, and negations. 2. The existential quantifier \(\exists x P(x)\) means "there exists at least one \(x\) in the domain such that \(P(x)\) is true." This can be expressed as a disjunction (OR) of \(P(x)\) evaluated at each element of the domain. 3. Since the domain is \{-2, -1, 0, 1, 2\}, we write: $$\exists x P(x) \equiv P(-2) \lor P(-1) \lor P(0) \lor P(1) \lor P(2)$$ 4. This means that \(\exists x P(x)\) is true if at least one of \(P(-2), P(-1), P(0), P(1), P(2)\) is true. 5. This expression uses only disjunctions (\(\lor\)) and the propositional function values, as required. Final answer: $$\exists x P(x) \equiv P(-2) \lor P(-1) \lor P(0) \lor P(1) \lor P(2)$$