Question

LetF(x, y) be the statement "xcan fooly," where the domain consists of all people ofthe world. Use quantifiers to express each of these statements.(a) Everybody can fool Fred.(b) Evelyn can fool everybody.(c) Everybody can fool somebody.(d) There is no one who can fool everybody.(e) No one can fool both Fred and Jennifer.(f) Nancy can fool exactly two people.

Answer 1

See steps below

Explanation:

Let F(x, y) and W be

F(x,y) = “x can fool y”

W the set of all the people in the world

a) Everybody can fool Fred.

`\forall x \in W,F(x, Fred)`

b) Evelyn can fool everybody.

`\forall y\in W, F(Evelyn, y)`

c) Everybody can fool somebody.

`\forall x \in W,\exists y :F(x,y)`

d) There is no one who can fool everybody.

`\\exists x \in W: \forall y ,F(x,y)`

e) No one can fool both Fred and Jennifer.

`\\exists x \in W: F(x,Fred)\wedge F(x,Jennifer)`

f) Nancy can fool exactly two people.

`\exists x,y \in W:\forall z\\eq x,z\\eq y, F(Nancy,x)\wedge F(Nancy,y)\wedge (\\eg F(Nancy,z))`