Philosophy 251: Handout #15
XXIV. For each of the following arguments construct
a derivation to prove that the argument is valid.
xRax 
xRxa,
~Rba / ~Raa
- x[ yRxy yRyx ], Raa / Rba
- x( Fx Gx
), x( Gx Hx
) / x( Fx Hx
).
- x( Fx Gx
), x( ( Gx v Hx ) Kx ) / x( Fx Kx )
- x( Fx Gx
) / xFx xGx
- x( ( Fx & Gx ) Hx ) / x( Fx Gx ) x( Fx Hx )
- / x( ~Bx ~Ax ) [ ~xBx ~xAx
]
- xyCxy / ( Caa & Cab ) & ( Cba
& Cbb )
- x( Ax Bx),
~Bc / ~Ac
- y[( Hy & Fy ) Gy ], zFz & ~xKxb / x( Hx Gx )
- xCx Ch / xCx
Ch
- x( ~Ax Kx ), y~Ky / w( Aw v ~Lwf )
- z(
Gz & Az ), y( Cy ~Gy ) / z( Az & ~Cz )
- x[( ~Cxb v Hx ) Lxx ], y~Lyy / xCxb
- xFx, zHz / ~y( ~Fy v ~Hy )
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