Philosophy 251: Handout #16

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

1. xAx / Aa & Ab
2. xyBxy, Bcd Ce / Ce
3. x( Dx Ex ), z( Ez Fz ) / Df Ff
4. zGz, x~Gx / ~Hg
5. x( Ix & ~Kx), Lh v Kj / xKx ( Ik & Lh )
6. Ma, Na / x( Nx & Mx )
7. Obbb / yOyby
8. xyPxy / wzPwz
9. xQx, zQz yRy / Rc
10. ~xSxx v zTz, Sdd / zUzzz v ( Te v yWy )

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

1. xRax xRxa, ~Rba / ~Raa
2. x[ yRxy yRyx ], Raa / Rba
3. x( Fx Gx ), x( Gx Hx ) / x( Fx Hx ).
4. x( Fx Gx ), x( ( Fx & Gx ) Hx ) / x( Fx Hx ).
5. x( Fx Gx ), x( ( Gx v Hx ) Kx ) / x( Fx Kx )
6. xFx & xGx / x( Fx & Gx )
7. x( Fx Gx ) / xFx xGx
8. x( ( Fx & Gx ) Hx ) / x( Fx Gx ) x( Fx Hx )
9. x( Dxx v Px ), y~Dyy, z( Pz Jz ) / w( Lwg v Pw )
10. / x( ~Bx ~Ax ) [ ~xBx ~xAx ]

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

1. xyCxy / ( Caa & Cab ) & ( Cba & Cbb )
2. x( Ax Bx), ~Bc / ~Ac
3. y[( Hy & Fy ) Gy ], zFz & ~xKxb / x( Hx Gx )
4. xCx Ch / xCx Ch
5. x( ~Ax Kx ), y~Ky / w( Aw v ~Lwf )
6. y[ Hy & ( Jyy & My )] / xJxb & xMx
7. z( Gz & Az ), y( Cy ~Gy ) / z( Az & ~Cz )
8. ~x( ~Rx & Sxx ), Sjj / Rj
9. x[( ~Cxb v Hx ) Lxx ], y~Lyy / xCxb
10. xFx, zHz / ~y( ~Fy v ~Hy )