Question

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. $\forall x\left(P\right(x)\to (G\left(x\right)\wedge S\left(x\right)\left)\right)$
• B. $\forall x\left(G\right(x)\wedge (S\left(x\right)\to P\left(x\right)\left)\right)$
• C. $\exists x\left(\right(G\left(x\right)\wedge S\left(x\right))\to P(x\left)\right)$
  
• D. $\forall x\left(\right(G\left(x\right)\vee S\left(x\right))\to P(x\left)\right)$

Answer 1

The correct option is D $\forall x\left(\right(G\left(x\right)\vee S\left(x\right))\to P(x\left)\right)$

The correct translation of "Gold and silver ornaments are precious" is choice (d)
$\forall x\left(\right(G\left(x\right)\vee S\left(x\right))\to P(x\left)\right)$
which is read as "if an ornament. is gold or silver, then it is precious",
Now since a given ornament cannot he both gold and silver at the same time.
Choice (b) $\forall x\left(\right(G\left(x\right)\wedge S\left(x\right))\to P(x\left)\right)$ is incorrect.