predicate logic and reasoning question

Question

I have been stuck on the following question for some time now and would appreciate if someone can provide some guidance on this matter. The question is as follows:

Use predicate logic reasoning techniques to solve the following problem: All academics who are computer scientists are programmers or mathematicians. Any logistician is a philosopher. Jack Jones is not a philosopher and he is not a programmer. Prove that if Jack Jones is a logistician he is not a computer scientist.

Answer 1

I'm not sure about this statement as being a if Jack is a logistician then he is a philosopher. It seems like you can derive a "reductio ad absurdam" (or contradiction) and get whatever you need as from a contradiction anything follows.

Not sure about this statement: "Any logistician is a philosopher. Jack Jones is not a philosopher and he is not a programmer. Prove that if Jack Jones is a logistician he is not a computer scientist."

CS - Computer science P - Programmer M - Mathematician L- Logistician H - Philosopher

1. All CS' are P v M. Assumption
2. All L are H. Assumption
3. No CS' are H. Assumption
4. Jack is not H and not CS. Assumption
5. Jack is an L.
6. If Jack is an L, Jack is a H.
7. Jack is an H. Contradiction lines 5 and 7
8. Therefore, Jack is L.
9. If Jack is an L, Jack is not CS'. 1, 8.
10. If Jack is not a CS, Jack is neither P v M. 1, 9.

Answer 2

Let $$A(x): x \textrm{ is an academician}.$$ $$C(x): x \textrm{ is a computer scientist}.$$ $$P(x): x \textrm{ is a programmer}.$$ $$L(x): x \textrm{ is a logistician}.$$ $$H(x): x \textrm{ is a philosopher}.$$

and let us denote Jack Jones by $a$. We have to prove that $$\forall x[(A(x)\wedge C(x))\rightarrow (P(x)\vee M(x))]\cdots(*)$$ $$\forall x[L(x)\rightarrow H(x)]\cdots (**)$$ $$\neg H(a), \neg P(a)$$ imply the conclusion $$L(a)\rightarrow \neg C(a).$$ From universal instantiation of $**$, $$L(a)\rightarrow H(a).$$ But $\neg H(a)$ and so $\neg L(a)$ and therefore $\neg L(a)\vee\neg C(a)$ i.e. $L(a)\rightarrow \neg C(a).$

Answer 3

We are told that Jack Jones is not a philosopher, so since all logisiticians are philosophers, it follows that Jack cannot be a logistician either. With that, any statement of the form 'If Jack is a logistician, then X' automatically becomes true, no matter what you fill in for X. That is, you can prove that If Jack Jones is a logistician, then he is a Flying Pig, and you can also prove that if Jack Jones is a logistician, then he is not a logistician. And we can certainly prove that if Jack ones is a logistician, then he is not computer scientist: