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GO Classes DA Test Series | Artificial Intelligence | Propositional and Predicate logic | Question: 9

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Which of the following formulas is a formalization of the sentence:
"Every connected and circuit-free graph is a tree"
Where $\operatorname{cir}(\mathrm{x})$ means " x has circuit".
  1. $\forall \mathrm{x}[(\operatorname{conn}(\mathrm{x}) \wedge \neg \operatorname{cir}(\mathrm{x})) \rightarrow \operatorname{tree}(\mathrm{x})]$
  2. $\neg \exists \mathrm{x}[(\operatorname{conn}(\mathrm{x}) \wedge \neg \operatorname{cir}(\mathrm{x})) \wedge \neg \operatorname{tree}(\mathrm{x})]$
  3. $\forall \mathrm{x}[(\operatorname{conn}(\mathrm{x}) \wedge \neg \operatorname{cir}(\mathrm{x})) \wedge \operatorname{tree}(\mathrm{x})]$
  4. $\forall \mathrm{x}[(\operatorname{conn}(\mathrm{x}) \wedge \operatorname{cir}(\mathrm{x})) \rightarrow \operatorname{tree}(\mathrm{x})]$

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Every connected and circuit-free graph is a tree

$\forall \mathrm{x}[(\operatorname{conn}(\mathrm{x}) \wedge \neg \operatorname{cir}(\mathrm{x})) \rightarrow \operatorname{tree}(\mathrm{x})]$ or

$\neg \exists \mathrm{x}[(\operatorname{conn}(\mathrm{x}) \wedge \neg \operatorname{cir}(\mathrm{x})) \wedge \neg \operatorname{tree}(\mathrm{x})]$
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