Exercise 8.14

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.