Symbolic Logic IPredicate Translations
Symbolize the following sentences, using the indicated letters.
1. Geraldine Ferraro is married. (f = "Geraldine Ferraro"; Mx = "x is married")
Mf
2. Walter Mondale is married. (m = "Walter Mondale")
Mm
3. In fact, Geraldine Ferraro and Walter Mondale both are married.
Mf Mm
4. But Ferraro isn't married to Mondale. (Rxy = "x is married to y")
~Rfm
5. So, obviously, Mondale isn't married to Ferraro.
~Rmf
6. Nevertheless, if Ferraro is married, so is Mondale.
Mf Mm
7. But if Ferraro is married, it's to John Zaccaro. (c = "John Zaccaro")
Mf Rfc
8. Anyway, Ferraro is married either to Mondale or Zaccaro.
Rfm v Rfc
9. Of Course, she isn't married to both of them.
~(Rfm Rfc) or ~Rfm v ~Rfc
10. And surely Zaccaro isn't married to both Ferraro and Jane Fonda.(j = "Jane Fonda")
~(Rcf Rcj) or ~Rcf v ~Rcj
Symbolize the following sentences, using quantifiers as needed.
1. All events have causes. (Ex = "x is an event"; Cx = "x has a cause")
x(Ex Cx)
2. Every event has a cause.
x(Ex Cx)
3. Not all events have causes.
~x(Ex Cx) or x(Ex ~Cx)
4. No events have causes.
x(Ex ~Cx) or ~x(Ex Cx)
5. All natural events have causes. (Nx = "x is natural")
x((Nx Ex) Cx)
6. All events that have causes are natural.
x((Ex Cx) Nx)
7. No unnatural events have causes.
x((~Nx Ex) ~Cx)
8. Some unnatural events are caused.
x((~Nx Ex) Cx)
9. No natural events are uncaused.
x((Nx Ex) ~~Cx) or ~x((Nx Ex) ~Cx) or x((Nx Ex) Cx)
10. Events are either natural or uncaused.
x(Ex (Nx v Cx))
11. Some natural events are uncaused.
x((Nx Ex) ~Cx)
12. Some uncaused events are unnatural.
x((~Nx Ex) ~Cx)
13. Some events are either uncaused or unnatural, but not both.
x(Ex ~(~Cx ~Nx))
Symbolize the following sentences, letting Ax = "x is an athlete";
Ox = "x is overpaid"; Ex = "x is an entertainer"; and Mx = "x is an employee".
1.Some athletes are overpaid.
x(Ax Ox)
2.Some athletes are not overpaid.
x(Ax ~Ox)
3.It's not true that some athletes are overpaid.
~x(Ax Ox)
4But it is true that some overpaid employees are not athletes.
x((Ox Mx) ~Ax
5.And there are employees who are neither athletes nor overpaid.
x(Mx ~(Ax v Ox))
6.Some employees are overpaid entertainers, but some are merely overpaid.
x(Mx (Ox Ex) y(My Oy)
7.Some nonathlete entertainers are neither overpaid nor employees.
x((~Ax Ex) & (~Ox & ~Mx))
8.Some employees are not athletes, nor are they entertainers or overpaid.
x(Mx (~Ax (~Ex ~Ox)))
Symbolize the following sentences, letting Sx = "x is a logic student"; Lx = "x is logical"; Px = "x is popular"; and j = "jane".
1. Logic students are logical.
x(Sx Lx)
2. No. Logic students definitely are not logical.
x(Sx ~Lx)
3. Well, not all logic students are logical.
~x(Sx Lx)
4.Anyway, it's true that those logic students who are logical are not popular.
x((Lx Sx) ~Px)
5.So if all logic students are logical, none of them is popular.
x(Sx Lx) y(Sy ~Py)
6.But if not all of them are logical, then not all of them are unpopular.
~x(Sx Lx) ~y(Sy ~Py)
7. If all logic students are logical, then if Jane is illogical she hasn't studied logic.
x(Sx Lx) (~Lj ~Sj)
8. And if Jane is both a logic student and illogical, then it's false either that logic students universally are logical or that the unpopular universally are logical.
(Sj ~Lj) ~{x(Sx Lx) v y(~Py Ly)}