# No-managers-are-sympathetic-philosophy-homework-help

Need assistance with the following textbook exercises (noted by A, B, C)

A)

Textbook Exercises 7.4: 1-10

Using the predicates listed for each assertion, â€œtranslateâ€ each of the following into quantified logical form.

1. No managers are sympathetic. (Mx, Sx)

2. Everything is in its right place. (Rx)

3. Some cell phones have no service here. (Cx, Sx)

4. Not everything is settled. (Sx)

5. Radiohead concerts are amazing. (Rx, Ax)

6. Nothing is everlasting. (Ex)

7. Not every earthquake is destructive. (Ex, Dx)

8. Very few people do not like Mac computers. (Px, Mx)

9. Only registered voters can vote in the next election. (Rx, Vx)

10. Not everyone disapproves (i.e., does not approve) of the president’s cabinet selections. (Ax)

B)

Textbook Exercises 7.6: 5-9

Translate each of the following arguments into quantified form and prove that each is valid using natural deduction. The letters that follow each argument give the predicate letters to use in symbolizing the argument.

5. If all store supervisors are wise, then some employees benefit. If there are some store supervisors who are not wise, then some employees benefit. As you can see, either way, some employees benefit. (S, W, E, B)

6. If someone studies philosophy, then all students benefit. If someone studies literature, then there are some students. So if someone studies philosophy and literature, then someone benefits. (P, B, L, S)

7. Everyone is a Democrat or a Republican, but not both. If someone is a Democrat, then she is a liberal or a conservative. All conservatives are Republican. So all Democrats are liberal. (D, R, L, C)

8. If there are any mavericks, then all politicians are committed to change. If there are any politicians, then anyone who is committed to change is pandering. So, if there are any mavericks, politicians are pandering. (M, P, C, A (for â€œpanderingâ€))

9. If everyone is a liberal, then no one is a conservative. There is a governor of Alaska and she is a conservative. So at least someone is not a liberal. (L, C, G)

C)

Textbook Exercises 7.9.1, 7.9.2: 6-12, 7.9.3: 1-6

7.9.1. Prove the following syllogisms valid first using natural deduction and then using the method of tableaux:

First Figure, Moods EAE, EIO

Second Figure, Moods AEE, AOO

Third Figure, Moods AII, OAO

Fourth Figure, Moods AEE, IAI

7.9.2. Construct formal proofs for all the arguments below. Use equivalence rules, truth functional arguments, and the rules of instantiation and generalization. These may also be proven using the method of tableaux.

6. âˆ€x(Cx âŠƒ Â¬Sx), Sa âˆ§ Sb âˆ´ Â¬(Â¬Ca âŠƒ Cb)

7. âˆƒxCx âŠƒ âˆƒx(Dx âˆ§ Ex), âˆƒx(Ex âˆ¨ Fx) âŠƒ âˆ€xCx âˆ´ âˆ€x(Cx âŠƒ Gx)

8. âˆ€x(Fx âŠƒ Gx), âˆ€x[(Fx âˆ§ Gx) âŠƒ Hx] âˆ´ âˆ€x(Fx âŠƒ Hx)

9. âˆƒxLx âŠƒ âˆ€x(Mx âŠƒ Nx), âˆƒxPx âŠƒ âˆ€x Â¬Nx âˆ´ âˆ€x[(Lx âˆ§ Px) âŠƒ Â¬Mx]

10. âˆ€x(Fx â‰¡ Gx), âˆ€x[(Fx âŠƒ (Gx âŠƒ Hx)], âˆƒxFx âˆ¨ âˆƒxGx âˆ´ âˆƒxHx

11. âˆƒx(Cx âˆ¨ Dx), âˆƒxCx âŠƒ âˆ€x(Ex âŠƒ Dx), âˆƒxEx âˆ´ âˆƒxDx

12. âˆ€x[(Â¬Dx âŠƒ Rx) âˆ§ Â¬(Dx âˆ§ Rx)], âˆ€x[Dx âŠƒ (Â¬Lx âŠƒ Cx)], âˆ€x(Cx âŠƒ Rx) âˆ´ âˆ€x(Dx âŠƒ Lx)

7.9.3. Using the method of tableaux, give an assignment of values for the predicates of each argument that shows that each argument is invalid.

1. âˆ€x(Ax âŠƒ Bx), âˆ€x(Ax âŠƒ Cx) âˆ´ âˆ€x(Bx âŠƒ Cx)

2. âˆƒx(Ax âˆ§ Bx), âˆ€x(Cx âŠƒ Ax) âˆ´ âˆƒx(Cx âˆ§ Bx)

3. âˆ€x[(Cx âˆ¨ Dx) âŠƒ Ex], âˆ€x[(Ex âˆ§ Fx) âŠƒ Gx] âˆ´ âˆ€x(Cx âŠƒ Gx)

4. âˆƒxMx, âˆƒxNx âˆ´ âˆƒx(Mx âˆ§ Nx)

5. âˆ€x[Dx âˆ¨ (Ex âˆ¨ Fx)] âˆ´ âˆ€xDx âˆ¨ (âˆ€xEx âˆ¨ âˆ€xFx)

6. âˆƒx(Cx âˆ§ Â¬Dx), âˆƒx(Dx âˆ§ Â¬Cx) âˆ´ âˆ€x(Cx âˆ¨ Dx)