### Artificial IntelligenceAIMA Exercises

True or false? Explain.
1. ${\exists\,x\;\;} x{Rumpelstiltskin}$ is a valid (necessarily true) sentence of first-order logic.
2. Every existentially quantified sentence in first-order logic is true in any model that contains exactly one object.
3. ${\forall\,x,y\;\;} xy$is satisfiable.

True or false? Explain.
1. ${\exists\,x\;\;} x{Rumpelstiltskin}$ is a valid (necessarily true) sentence of first-order logic.
2. Every existentially quantified sentence in first-order logic is true in any model that contains exactly one object.
3. ${\forall\,x,y\;\;} xy$is satisfiable.

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