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.
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.