PHH 2130: Formal Logic I

Continuation of Additional Problems for Predicate Logic

1. No athletes are bookworms. Carol is a bookworm. Therefore, Carol is not an athlete. (Ax, Bx, c)

2. All dancers are exuberant. Some fencers are not exuberant. Therefore, some fencers are not dancers. (Dx, Ex, Fx)

3. 1. (x)(Bx --> Cx) 4. 1. (x)[Jx --> (Kx . Lx)]

2. (Ex)(Ax . Bx) 2. (Ey)-Ky/ (Ez)-Jz

/ (Ex)(Ax . Cx)

5. 1. (x)[Ax --> (Bx v Cx)] 6. 1. (Ex)Ax --> (x)(Bx -->Cx)

2. (Ex)(Ax . -Cx) 2. Am . Bm/ Cm v (x)Ax

/ (Ex)Bx

7. All gardeners are industrious. Furthermore, anyone industrious is respected. Arthur and Catherine are gardeners. It follows that they are respected. (Gx, Ix, Rx, a, c)

8. 1. (Ex)-Ax v (Ex)-Bx 9. 1. (x)(Ax . Bx) v (x)(Cx . Dx)

2. (x)Bx/ -(x)Ax 2. -(x)Dx/ (x)Bx

10. 1. -(Ex)(Ax . -Bx) 11. 1. (x)(Fx --> Gx)

2. -(Ex)(Bx . -Cx) 2. Hh --> Fg/ Hh --> Gg

/ (x)(Ax --> Cx)

12. 1. -Oa 13. 1. (x)(y)(Fxy . Fya)/ Faa

2. (x)(y)[(Mx v Py) --> (Oa v Ob)]/ Ma --> Ob

14. Use conditional proof

1. (x)[(Bx v Gx) --> Fx]

2. (x)[(Fx v Vx) --> Nx]/ (x)(Bx --> Nx)

15. A communist is either a fool or a knave. Fools are naive. Not all communists are naive. Therefore, some communists are knaves.

16. Use conditional proof

1. (x)(Px --> Lx)

2. (x)[(Lx . Px) --> Sx]/ (x)[Px --> (Lx . Sx)]

17. 1. -(Ex)(Fx . Gx) 18. Use conditional proof

2. (x)[Hx --> (Fx --> Gx) 1. (x)[Sx --> (Tx --> Ux)]

/ -(Ex)(Hx . Fx) 2. (x)[Ux --> (Vx . Wx)]

/ (x)[Sx --> (Tx --> Vx)]

19. Use indirect proof 20. Use indirect proof

1. (Ex)Rx 1. -(Ex)Ax/ (Ex)(Ax --> Gx)

2. (x)(-Gx --> -Rx)

3. (Ex)Mx/ (Ex)Gx . (Ex)Mx