Logic Philosophy question

I am looking for help in answering the full question with a full conditional proof (cp). This will help me understand this question and others that I am trying to understand. Thank you.

Would anyone know how to construct a Conditional Proof for this argument?

(∃x) (Wx • Jx), (x) (Ax → ~Jx) ∴ (∃x) (Wx • ~Ax)

I cannot figure it out. Any help will be greatly appreciated!

This is what I have. Are there errors anywhere? This is what seems to be the rules we have to follow for my work. Thank you!

Proof using Conditional proof (CP) 1. (∃x) (Wx • Jx) 2. (x) (Ax → ~Jx) // (∃x) (Wx • ~Ax)

``````3. Wx           Assumption for Conditional Proof
4, Ax → ~Jx     2, Reiteration
5, Ab → ~Jb     4, Existential Instantiation
6, ~Jb          5, Modus Tollens
7. Wx • Jx      1, Reiteration
8. Wc • Jc      7, Existential Instantiation
9. Jc           8, Simplification
10. ∃x Jc       9, Existential Generalization
11. Ax → Jx     2, Universal Instantiation
12. ~Jb         5, 6 Modus Tollens
13. (Wx • Jx)   1, Reiteration
14. Wx          14, Simplification
``````

15, (∃x) (Wx • ~Ax) 3-14 CP

• There are errors everywhere! Many of the inferences you have made are invalid, and often serve no purpose. Besides that, a Conditional Proof is not the appropriate build to prove a statement that does not contain a conditional. Oct 17, 2019 at 23:08
• Thank you for your reply. According to the instructions I was given we have to translate the argument into the symbolism of predicate logic. Use one of the proof techniques to demonstrate the validity of the argument. It has to be shown in RAA and CP. I was able to do the RAA, but CP is very difficult for me. I understand in the real world they may serve no purpose, and CP might not be an appropriate build to prove the statement, but it's what we were instructed to do. With that information can anyone help me understand what I did wrong? I can't find anything to help me. THANK YOU! Oct 18, 2019 at 16:04
• Can you write with ordinary language words and your own diagram something to help you plan your overall strategy, and then sit back and see how you can use the available rules to implement the strategy? The key step seems to be the contrapositive, but it may require more than one step using the transformation rules available to you. Maybe the following example of applying the contrapositive will inspire you to do it without involvement of a mico-managing supervisor: matheducators.stackexchange.com/questions/17368/… Nov 1, 2019 at 2:51