Homework for Tuesday, April 30

Love and Marriage Symbolizations

(see http://phil-rlst.claremontmckenna.edu/akind/Logic01s/lovesym.htm)

Countermodels

q Exercise 4.2 xi – xv

q Plus the following:

1. $x(~Cx & Fx), "x(Cx ® Fx) |- $xCx ® $xBx

2. ~"x(Cx ® Bx), "x(Bx ® Dx), $xCx ® $xBx |- "x(Cx Ú Dx)

3. "x(Fx & Gx ® Hx), $x((Fx & Hx) & ~Gx), $x(Gx & ~Hx) |- ~$x(Fx & Gx)

Proofs

1. "x$y~(Fx Ú Gy) |- ~"x(Gx Ú Fx)

2. "y$x(Fy & Kx), "y(Ky ® ~Hy) |- ~"x(Fx ® Hx)

3. $x~Fx ® "x(Hx ® Gx), $xHx |- "xFx Ú $xGx

4. "x(Fx Ú Gx), "x(Fx ® Hx), ~"xGx |- $xHx

5. "x(Fx & (Gx Ú Kx)), ~$x(Kx « Fx) |- "x(Fx & Gx)

6. $x(Fx Ú Gx), $xFx ® "xHx, $xGx ® ~$xHx |- ~($xHx & $x~Hx)

7. "xFx Ú $xGx |- $x(Fx Ú Gx)