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:
$$G\left( x \right):\,\,x$$ is a gold ornament.
$$S\left( x \right):\,\,x$$ is a silver ornament.
$$P\left( x \right):\,\,x$$ is precious.

Consider the following well-formed formulae:

$${\rm I}.$$ $$\,\,\neg \forall x\left( {P\left( x \right)} \right)$$
$${\rm I}{\rm I}.\,\,\,\,\,\,\neg \exists x\left( {P\left( x \right)} \right)$$
$${\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,\neg \exists x\left( {\neg P\left( x \right)} \right)$$
$${\rm I}V.\,\,\,\,\,\,\exists x\left( {\neg P\left( x \right)} \right)$$

Which of the above are equivalent?

The binary operation ◻ is defined as follows:

Which one of the following is equivalence to $$P \vee Q$$?

Which of the following is the negation of $$$\left[ {\forall x,\alpha \to \left( {\exists y,\beta \to \left( {\forall u,\exists v,\gamma } \right)} \right)} \right]?$$$