# Quantifier Problems

```A. {1} 1. (x)(Ax -> -Cx)      P      / Wa -> ((x)(Wx -> Cx) -> -Aa)

B. {1} 1. (x)(Px -> Gx)       P
/ (x)(((Dx & Ex) & (y)((Py & Ey) -> -Gy)) -> -Px)

C. {1} 1. (x)(Ax -> Gx)          P
{2} 2. (x)(Cx -> Hx)          P       / (x)(Gx -> Cx) -> (x)(Ax -> Hx)

D. {1} 1. (x)Gx -> (x)(Cx -> Gx)    P
{2} 2. (x)Tx -> (x)(Gx -> Tx)    P   / (x)(Tx & Gx) -> (x)(Cx -> Tx)

E. {1} 1. (x)(Sxi -> Vxj)      P
{2} 2. (x)(-Fhx -> -Vax)    P
{3} 3. (x)(Fxk -> -Fxj)     P        / Fhk -> -Sai

F. {1} 1. (x)(y)((z)Fzy -> Gx)    P
{2} 2. (x)Hx                   P      /  (x)(Hx -> -Gx) -> -Fac

G. {1} 1. (x)(Rx -> (Sx v Mx))      P
{2} 2. (x)((Ux & Rx) -> -Sx)     P    / (x)(Ux -> Rx) -> (y)(Uy -> My)

H. {1} 1. (x)(Lx -> ((y)(Py -> Vy) -> Mx))     P
{2} 2. (z)(Pz & Vz) -> (y)(Py -> Vy)       P
/ (x)Lx -> ((z)(Pz & Vz) -> (y)My)

I. {1} 1. (x)(Fxa -> Fxb)    P      / (x)(y)((Kxy & Fya) -> Fyb)

J. {1} 1. (x)((y)(Byb & Lxyb) -> Fx)      P
{2} 2. (x)(Cxb & Lxab)                 P  / (x)(Cxb -> -Fx) -> -Bab

K. {1} 1. (x)((y)(z)((Gz & -Rz) & Sxzy) -> Cx)          P
{2} 2. (z)((Wz & Orz) -> (Slzr v Smzr))                P
/ (z)((Wz & Orz) & (Gz & -Rz)) -> ((u)-Smur -> Cl)

L. {1) 1. (x)((Px & -Rxx) -> (y)(Py -> -Ryx))          P
{2} 2. (y)(Py -> (x)((Px & -Ryx) -> -Hyx))          P
/ (x)((Px & (z)(Pz -> -Rxz)) -> (y)(Py -> -Hyx))

```