Philosophy 251: Handout #17
XXXVII. For each of the following
arguments construct a derivation to prove that the argument is
valid.
x( Zx 
yKy
) /
x[ Zx 
y(
Ky v Sy )]
x~
y(
Rxy & ~Uy) 
x(
Px & Jx ),
x~
y( ~Uy & Rxy ) / ~
x( Px
~Jx )
x( Hx
Fx
),
x[( Fx & Uxx )
Wxx ],
zUzz /
x( Hx
Wxx )
x[( Fx & Gx )
y( Axy & Py )],
x
y[ Fx & ( Axy & Py )] /
x(
Fx & Gx )
x( Lx
Yx
),
x( Cx & Yx ) &
x( Cx & ~Yx ) / ~
x( Cx
Lx )
x( Px
Qx
) / (
xPx &
xQx )
x( Px & Qx )
x
y[( Ry v Dx )
~Ky ],
x
y( Ax
~Ky ),
x( Ax v Rx ) /
x~Kx
y( My
Ay
),
x
y[( Bx & Mx) & (Ry & Syx
)],
xAx 
y
z(
Syz
Ay )
/
x( Rx & Ax )
x
y[( Hky & Hxk )
Hxy ],
z( Bz
Hkz ),
x( Bx & Hxk )
/
z[ Bz &
y( By
Hzy )]
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.
x( ~Bx
~Wx ),
xWx /
xBx
x
y
zGxyz /
x
y
z( Gxyz
Gzyx )
x( Hx 
yRxyb
),
x
z( Razx
Sxzz ) / Ha 
xSxcc
- ~
x( Fx & Aix )
~
xKx ,
y[
x~( Fx & Aix ) & Ryy ] / ~
xKx
z( ~Lz v
yKy ) /
zLz
yKy
x(
Jxa & Ck ),
x( Sx & Hxx ),
x[(
Ck & Sx )
~Ax
] /
z( ~Az & Hzz )
x[
Cx v
y( Wxy
Cy )],
x( Wxa & ~Ca ) /
xCx
x
y( Dxy
Cxy ),
x
yDxy,
x
y( Cyx
Dxy ) /
x
y( Cxy & Cyx )
- /
x( Ax
Bx ) 
x( ~Bx
~Ax )
- /
x[ Cx
( Cx
Dx )]
x( Cx
Dx
)
- / ~
x( Ex v Fx )
x~Ex
- /
x( Gx
Hx ) v
xGx
- / (
xJx
xKx ) 
x(
Jx
Kx )
- /
x( Lx
Mx )
~
x[(
~Lx v ~Mx ) & ( Lx v Mx )]
- /
x
y( Nx v Oy )
y
x( Nx v Oy )
Back
to Syllabus