Let Graph(x) be a predicate which denotes that x is a graph. Let Connected(x) be a predicate which denotes that x is connected. Which of the following first order logic sentences DOES NOT represent the statement: “Not every graph is connected”?
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$\lnot \forall x\, \Bigl ( Graph(x) \implies Connected(x) \Bigr )$
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$\exists x\, \Bigl (Graph(x) \land \lnot Connected(x) \Bigr )$
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$\lnot \forall x \, \Bigl ( \lnot Graph(x) \lor Connected(x) \Bigr )$
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$\forall x \, \Bigl ( Graph(x) \implies \lnot Connected(x) \Bigr )$
D
Correct answer
Explanation
Vx[ Graph (x) $\Rightarrow$7 connected (x) ]
Indicates “for every x if x is a graph, then it is not connected”