Consider the statement “Not all that glitters is gold” Predicate $glitters(x)$ is true if $x$ glitters and predicate $gold(x)$ is true if $x$ is gold. Which one of the following logical formulae represents the above statement?

The statement "Not all that glitters is gold" can be written as the negation of "All things that glitter are gold":

$$eg (\forall x (glitters(x) \Rightarrow gold(x)))$$

Using the logical equivalence $P \Rightarrow Q \equiv eg P \vee Q$:

$$eg (\forall x ( eg glitters(x) \vee gold(x)))$$

Applying De Morgan's Law for quantifiers:

$$\exists x eg ( eg glitters(x) \vee gold(x)) \equiv \exists x (glitters(x) \wedgeeg gold(x))$$

This means "there exists something that glitters and is not gold", which corresponds to option (D).