Deductive logic problem...

Question

if amy takes a job at starbucks she will be working too hard. if she takes a job at safeway she will not be appreciated. if she is either working too hard or not appreciated, she will not be happy.

if she works for dkny then she will be well paid.

obviously she will take a job at either safeway, starbucks or dkny.

therefore if amy is happy, she is well paid

Answer 1

appreciation, hard work, and pay scale are not flip sides of the same coin.  Saying one job will cause you to work too hard has no bearing on you being appreciated or well paid.  Due to the lack of continuity between attributes, the conclusion that happiness means being well paid cannot be made.  It may be true for a single instance where the paycheck is a side effect, but it is not the happiness that directly correlates to the paycheck.

Answer 2

The argument is valid. If the premises are true, then the conclusion must necessarily be true.

Symbolization Key:

B = Amy takes a job at Starbucks

W = Amy takes a job at Safeway

D = Amy works for DKNY

A = Amy will be appreciated (~A = Amy will not be appreciated)

T = Amy will be working too hard

H = Amy will be happy (~H = Amy will not be happy)

P = Amy will be well paid

Symbolized Argument:

P1. B -> T

P2. W -> ~A

P3. (T v ~A) -> ~H

P4. D -> P

P5. (W v B) v D

C: H -> P

Proof:

1. B -> T                    

2. W -> ~A                    

3. (T v ~A) -> ~H              

4. D -> P                    

5. (W v B) v D............./H -> P

6. ~T -> ~B................1, Trans

7. ~~A -> ~W.............2, Trans

8. A -> ~W.................7, DN

9. ~(T v ~A) v ~H.........3, Impl

10. ~H v ~(T v ~A).......9, Com

11. ~H v (~T & ~~A)....10, DM

12. ~H v (~T & A)........11, DN

13. (~H v ~T) & (~H v A)..12, Dist

14. (~H v A) & (~H v ~T)..13, Com

15. ~H v ~T.................13, Simp

16. ~H v A..................14, Simp

17. H -> ~T.................15, Impl

18. H -> A..................16, Impl

19. H -> ~W................8,18, HS

20. ~~(W v B) v D........5, DN

21. ~(W v B) -> D........20, Impl

22. (~W & ~B) -> D.....21, DM

23. ~W -> (~B -> D)....22, Exp

24. H -> (~B -> D).......19,23, HS

25. (H & ~B) -> D........24, Exp

26. (~B & H) -> D........25, Com

27. ~B -> (H -> D).......26, Exp

28. ~T -> (H -> D)........6,27, HS

29. H -> (H -> D).........17,28, HS

30. (H & H) -> D..........29, Exp

31. H -> D..................30, Taut

32. H -> P..................4,31, HS

Answer 3

If Amy doesn't care about money, then working for DKNY won't actually make her happy.

Therefore, you are missing a premise:

"If Amy is well paid, then she is happy."

Furthermore, she may be well-paid, but what if she works too hard for that money? Then she will not be happy, as stated above.

Your conclusion also doesn't follow. If all Amy cares about is money, then happiness would be a result of being well-paid. However, if she cares about anything else, she could be happy even if she doesn't make much money.

All that your premises really determine is that she won't be happy working at Starbucks or Safeway.

Answer 4

In logic, this is the usual way they represent the problem:

Where SB - starbucks, WH - working hard, SW - safeway, ~A - not appreciated, ~H is not happy, D is DKNY and P is paid:

if SB, then WH

if SW, ~A

if WH v ~A, ~H

if D, then P

either SW v SB v D

thus, if H then P

DKNY indeed!

Answer 5

Hi

Starbucks= working hard

Safeway= Unappreciated

Dkny=well paid

Not  happy = Unappreciated or working hard

Well Paid =X

Well paid is equal to x because it could be happy or working hard or Unappreciated or a combination of any of the three . There are people who make millions that are not happy so well paid cannot automatically equal  happy .

Hope this helps

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Answer 6

take the job at dkny

Answer 7

Your conclusion only follows because of the artificial condition that Amy must take a job at one of the three businesses.

Furthermore, based on these premises, a job at DKNY doesn't guarantee her happiness. It's just her only chance of being happy within the restricted set of choices allowed.

The logic is entirely valid, but it demonstrates the occasional uselessness of deductive logic when the premises are unreasonably gimmicked to force the desired conclusion.