Q22

MCQ2 marks, −0.5

Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ is connected. Which of the following first order logic sentences DOES NOT represent the statement: $\qquad\text{“Not every graph is connected"}$

(A)

$\lnot \forall x\, \Bigl (\text{ Graph}(x) \implies \text{ Connected}(x) \Bigr )$

(B)

$\exists x\, \Bigl (\text{ Graph}(x) \land \lnot \text{ Connected}(x) \Bigr )$

(C)

$\lnot \forall x \, \Bigl ( \lnot \text{ Graph}(x) \lor \text{ Connected}(x) \Bigr )$

(D)

$\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$

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