Consider the statement “Not all that glitters is gold” Predicate…
2014
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?
Answer: D. \(\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)\) — Correct formula: ∃x: glitters(x) ∧ ¬gold(x) Why this matches the sentence: "Not all that glitters is gold" means there is at least one thing that glitters but…
- A.
\(\forall x: \text{glitters} (x)\Rightarrow \neg \text{gold}(x)\) - B.
\(\forall x:\text{gold} (x)\Rightarrow \text{glitters}(x)\) - C.
\(\exists x: \text{gold}(x)\wedge \neg \text{glitters}(x)\) - D.
\(\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)\)
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Show answer & explanation
Correct answer: D
Correct formula: ∃x: glitters(x) ∧ ¬gold(x)
Why this matches the sentence:
"Not all that glitters is gold" means there is at least one thing that glitters but is not gold.
Formally, this is the negation of the universal implication: ¬∀x (glitters(x) ⇒ gold(x)), which is equivalent to ∃x (glitters(x) ∧ ¬gold(x)).
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