Philosophy 251: Handout #16
XXV. 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( 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( 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( Fx & Aix )
~
xKx ,
y[
x~( Fx & Aix ) & Ryy ] / ~
xKx
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( Ex v Fx )
x~Ex
- / (
xJx
xKx ) 
x(
Jx
Kx )
- /
x
y( Nx v Oy )
y
x( Nx v Oy )
x{( Fx & ~Kx ) 
y[( Fy & Hyx ) & ~Ky ]},
x[( Fx &
y[( Fy & Hyx )
Ky ])
Kx ]
Mp / Mp
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