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 A. forall x [G(x) ^ S(x) -> P(x)] B. forall x [G(x) v S(x) -> P(x)] C. exists x [G(x) ^ S(x) -> P(x)] D. forall x [G(x) -> P(x)] ^ forall x [S(x) -> P(x)]

GATE 2009 · Discrete Mathematics · First Order Logic · easy

Answer: D. forall x [G(x) -> P(x)] ^ forall x [S(x) -> P(x)]

1. Translate 'all gold ornaments are precious': forall x (G(x) -> P(x)): every gold ornament is precious.
2. Translate 'all silver ornaments are precious': forall x (S(x) -> P(x)): every silver ornament is precious.
3. Combine both claims: [forall x (G(x) -> P(x))] ^ [forall x (S(x) -> P(x))]. This is option D. Note: option B is logically equivalent but D is most explicit.