PL 330  Advanced unicodeic Logic

Prenex Form Exercises

Each of the following schemata is in either purified or mixed form.  Transform each schema into prenex form. 

1.    (x)Dx (y)(Py By)

2.    ~(x)Dx (y)(Py ~By)

3.    (x)[[Dx (y)(Py ~By)] ~Cx]

4.    (x)(Bx Yx) (y)(By Ry)

5.    (x)[(Bx Rx) Yx] (y)(Yy Ry)

6.    (x)[(Sx Wx) [(y)(Wy Fy) Fx]]

7.    (x)[(Ex Lx) [(y)(Py ~Fy) ~Sx]]

8.    [(x)(Ex Lx) (y)(Py ~Fy)] (z)(Ez ~Sz)

9.    (x)[(Ex Lx) [(y)(Py ~Fy) ~Sx]]

10.    (∀x)[(Hx ~Sx) [(y)(Wy Ay) Ux]]

11.    (x)[Dx Mx : (y)(Ty ~Lxy)]

12.    (∀x)[(Dx Mx) ~(y)(Ty Lxy)]

13.    (x)[(~Ax Lx) (y)((Ay Dy) Mxy]

14.    (x)[[Bx (y)(Txy Ly)] (z)[Txy (u)~Buz]]

15.    (x)[Px [(y)[Dy Hxy (z)[(Pz Vzx) Byz]] (u)(Nu Mxu)]]]

Solutions