Some Problems to Work on
In Reviewing for the Final
 

Difficult Practice Proofs
You should be able to do all of S77-S100, as well as the homework problems assigned for 5/4/99.  For some difficult practice proofs try the following:

1. @x$y(Fx -> Gy)|-$y@x(Fx -> Gy)
2. @x(Fx <-> Gx v Hx), $xGx, @x(Fx -> @yHy) |- @xFx
3. Ha & $x~Fx, $xGx -> @xFx, @x(Hx -> Jx) |- $x(~Gx & Jx)
4. $x(Px v Qx), @x(Px -> Kx), @x(Qx -> Kx)|-$xKx
5. $x(Fx & Hx) v @x(Jx -> Gx), @x(Fx -> ~Hx) |- $xJx -> $x(Gx & Jx)
6. $x(Fx v Gx), $xFx -> @xHx, $xGx -> ~$xHx |- ~($xHx & $x~Hx)
7. @xFx v $xGx |- $x(Fx v Gx)
 

Indirect Truth Table Practice.
3 of the following 5 sequents are valid.

1.  ~(P <-> Q), P v (R v S) |- ~R & Q -> S
2.  P v Q -> R, R & S <-> ~Q, S & P |- Q & R
3.  P v R -> Q, ~(R <-> S), R -> ~Q |- P -> S
4.  ~(P v Q), R -> S, ~S v Q |- Q <-> R
5.  P -> ~R, Q & R <-> S |- P <-> ~S
 

Some Interesting Symbolizations to Think About

  1. Every human has a parent, but not every human is a parent.  (Hx: x is human;  Pxy: x is the parent of y)
  2. Symbolize the intended meaning of the following sign often seen hanging in restaurants: "No shirt, no shoes, no service." (Gx: x gets service;  Sx: x wears shoes; Tx: x wears a shirt)
  3. Symbolize the intended meaning of the following sign often seen on a freeway lane: "Exit Only" (i.e., symbolize "this lane is an exit only lane.")  (a: this lane, Ex: x must exit; Lx: x is a lane; Ixy: x is in y.)
 

For more predicate logic symbolization practice, try the following worksheets:

For practice with sentential logic symbolizations, print yourself out a fresh copy of the X-Files or Friendly symbolization worksheets.