Consider the statement “Not all that glitters is gold” Predicate…

GATE · 2014 · CS · Set 1 · Computer Science & IT

Consider the statement

“Not all that glitters is gold”

Predicate glitters(x)glitters(x) is true if xx glitters and predicate gold(x)gold(x) is true if xx is gold. Which one of the following logical formulae represents the above statement?

  1. A.

    ∀x:glitters(x)⇒¬gold(x)\forall x: \text{glitters} (x)\Rightarrow \neg \text{gold}(x)

  2. B.

    ∀x:gold(x)⇒glitters(x)\forall x:\text{gold} (x)\Rightarrow \text{glitters}(x)

  3. C.

    ∃x:gold(x)∧¬glitters(x)\exists x: \text{gold}(x)\wedge \neg \text{glitters}(x)

  4. D.

    ∃x:glitters(x)∧¬gold(x)\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)

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