Philosophy 251: Handout #17

XXXVII. For each of the following arguments construct a derivation to prove that the argument is valid.

1. x( Zx yKy ) / x[ Zx y( Ky v Sy )]
2. x~y( Rxy & ~Uy) x( Px & Jx ), x~y( ~Uy & Rxy ) / ~x( Px ~Jx )
3. x( Hx Fx ), x[( Fx & Uxx ) Wxx ], zUzz / x( Hx Wxx )
4. x[( Fx & Gx ) y( Axy & Py )], xy[ Fx & ( Axy & Py )] / x( Fx & Gx )
5. x( Lx Yx ), x( Cx & Yx ) & x( Cx & ~Yx ) / ~x( Cx Lx )
6. x( Px Qx ) / ( xPx & xQx ) x( Px & Qx )
7. xy[( Ry v Dx ) ~Ky ], xy( Ax ~Ky ), x( Ax v Rx ) / x~Kx
8. y( My Ay ), xy[( Bx & Mx) & (Ry & Syx )], xAx yz( Syz Ay )
   / x( Rx & Ax )
9. xy[( Hky & Hxk ) Hxy ], z( Bz Hkz ), x( Bx & Hxk )
   / z[ Bz & y( By Hzy )]
10. x{( Fx & ~Kx ) y[( Fy & Hyx ) & ~Ky ]},
    x[( Fx & y[( Fy & Hyx ) Ky ]) Kx ] Mp / Mp

XXXVIII. For each of the following arguments construct a derivation to prove that the argument is valid.

1. x( ~Bx ~Wx ), xWx / xBx
2. xyzGxyz / xyz( Gxyz Gzyx )
3. x( Hx yRxyb ), xz( Razx Sxzz ) / Ha xSxcc
4. ~x( Fx & Aix ) ~xKx , y[ x~( Fx & Aix ) & Ryy ] / ~xKx
5. z( ~Lz v yKy ) / zLz yKy
6. x( Jxa & Ck ), x( Sx & Hxx ), x[( Ck & Sx ) ~Ax ] / z( ~Az & Hzz )
7. x[ Cx v y( Wxy Cy )], x( Wxa & ~Ca ) / xCx
8. xy( Dxy Cxy ), xyDxy, xy( Cyx Dxy ) / xy( Cxy & Cyx )
9. / x( Ax Bx ) x( ~Bx ~Ax )
10. / x[ Cx ( Cx Dx )] x( Cx Dx )
11. / ~x( Ex v Fx ) x~Ex
12. / x( Gx Hx ) v xGx
13. / ( xJx xKx ) x( Jx Kx )
14. / x( Lx Mx ) ~x[( ~Lx v ~Mx ) & ( Lx v Mx )]
15. / xy( Nx v Oy ) yx( Nx v Oy )