Question

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?

• A. $\forall x:glitters\left(x\right)\Rightarrow \neg$gold(x)
• B. $\forall x:gold\left(x\right)\Rightarrow \neg$glitters(x)
• C. $\exists x:gold\left(x\right)\wedge \neg$glitters(x)
• D. $\exists x:glitters\left(x\right)\wedge \neg$ gold(x)

Answer 1

The correct option is D $\exists x:glitters\left(x\right)\wedge \neg$ gold(x)

(a) $\forall xglitters\left(x\right)\Rightarrow \neg$gold(x)
All glitters are not gold
(b) $\forall xgold\left(x\right)\Rightarrow$glitters(x)
All golds are glitters
(c) $\exists xgold\left(x\right)\wedge \neg$glitters(x)
There exist gold which is not glitter i.e. not all golds are glitters.
(d) $\exists xglitters\left(x\right)\wedge \neg$ gold(x)
Not all that glitters is gold i.e., there exist some which glitters and which is not gold.