Project ForgeWhich one of the following is the most appropriate logical formula to represent the statement: "Gold and silver ornaments are precious". Using G(x): x is a gold ornament, S(x): x is a silver ornament, P(x): x is precious.
- A∀x(P(x) → (G(x) ∧ S(x)))
- B∀x((G(x) ∧ S(x)) → P(x))
- C∃x((G(x) ∧ S(x)) → P(x))
- ∀x((G(x) ∨ S(x)) → P(x))
Explanation
The natural-language "gold and silver ornaments are precious" means every gold ornament is precious AND every silver ornament is precious — i.e. anything that is EITHER a gold OR a silver ornament is precious. This translates to ∀x((G(x)∨S(x))→P(x)), not a conjunction inside the antecedent (which would incorrectly require an ornament to be both gold AND silver simultaneously).
Source: GATE CS 2009 (2009)
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