Correct : a

Identify the Predicates:
• `glitters(x)`: x glitters.
• `gold(x)`: x is gold.

Translate the Statement:
"All that glitters is gold" means:
    ∀x (glitters(x) → gold(x))

Therefore, "Not all that glitters is gold" is:
    ¬∀x (glitters(x) → gold(x))

Using the equivalence:
    ¬∀x P(x) ≡ ∃x ¬P(x)
we get:
    ∃x ¬(glitters(x) → gold(x))

Since:
    ¬(A → B) ≡ A ∧ ¬B
the formula becomes:
    ∃x (glitters(x) ∧ ¬gold(x))

This means: "There exists at least one thing that glitters but is not gold."

Compare with the Given Options:
• A) ∃x: gold(x) ⇒ ¬glitters(x)
    Means there exists something such that if it is gold, it does not glitter.

• B) ∃x: glitters(x) ⇒ ¬gold(x)
    This is the intended answer among the given options, but strictly speaking, it is not logically equivalent to the required formula because an implication can be true when `glitters(x)` is false.

• C) ∀x: gold(x) ⇒ glitters(x)
    Means "All gold things glitter."

• D) ∀x: glitters(x) ⇒ ¬gold(x)
    Means "Nothing that glitters is gold," which is stronger than the given statement.

Conclusion:
The mathematically precise formula is:

∃x (glitters(x) ∧ ¬gold(x))

Since this exact formula is not provided, Option B is the intended answer in the given choices.