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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?

1. ∀x: glitters(x) ⇒ ¬gold(x)
2. ∀x: gold(x) ⇒ glitters(x)
3. ∃x: gold(x) ∧ ¬glitters(x)
4. ∃x: glitters(x) ∧ ¬gold(x)

Correct answer: ∃x: glitters(x) ∧ ¬gold(x)

Solution

The correct option indicates that there exists at least one object that glitters but is not gold, which directly aligns with the meaning of the statement 'Not all that glitters is gold.' This captures the essence that some glittering objects do not possess the quality of being gold.

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