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Which one of the following is the most appropriate logical formula to represent the statement: "Gold and silver ornaments are precious" The following notations are used: G(x): x is a gold ornament. S(x): x is a silver ornament. P(x): x is precious.

1. ∀x(P(x) → (G(x) ∧ S(x)))
2. ∀x(((G(x) ∧ S(x)) → P(x)))
3. ∃x(((G(x) ∧ S(x)) → P(x)))
4. ∀x(((G(x) ∨ S(x)) → P(x)))

Correct answer: ∀x(((G(x) ∨ S(x)) → P(x)))

Solution

The correct option states that for all x, if x is either a gold or a silver ornament, then x is precious. This accurately captures the idea that both types of ornaments are considered precious.

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