I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove each step?) Using only inference rules, reit, quantifier rules. What have I missed writing out?

• My calculation was completely wrong so look directly at grahams comment and what he has put up for correct explanations!
– user39869
Jun 6, 2019 at 3:26
• This is the third context-less question you've asked about Fitch-style proofs. Jun 6, 2019 at 3:52

On line 9 referencing conjunction elimination from line 8 should derive either B(a) or K(a), but not R(a).

You might start this with the assumption on line 8 which is made to hopefully eliminate the existential in line 2.

Then use conjunction elimination to derive B(a) from that assumption. Use universal elimination from line 1 to derive B(a) → R(a). Those two lines allow one to derive R(a). Use conjunction elimination to get K(a) and then conjunction introduction to combine R(a) ∧ K(a). Use existential introduction to turn that into ∃x(R(x) ∧ K(x)).

That will allow you to discharge the assumption using existential elimination to complete the proof.

Here's the skeleton for the proof. You begin by assuming a witness to the existential in the premises, aiming to derive a witness for the existential in the conclusion.

``````  |  Ɐx (Bx → Rx)      Premise
|_ Ǝx (Bx ˄ Kx)      Premise
|  |_ [c] Bc ˄ Kc    Assumption
|  |  :              ˄E
|  |  :              ˄E
|  |  :              ⱯE
|  |  :              →E
|  |  Kc ˄ Rc        ˄I
|  |  Ǝx (Kx ˄ Rx)   ƎI
|  Ǝx (Kx ˄ Rx)      ƎE
``````
• thank you so much graham! Could you please tell me the : steps as well and which steps I should higlight to each step?
– user39869
Jun 6, 2019 at 0:20
• Please, try to do it for yourself first. @maxpax Jun 6, 2019 at 0:26
• I did, and the way I tried it turned out like the one above, so I'm completely lost and not sure what to do? Unfortunately, I'm not gifted in this at all.
– user39869
Jun 6, 2019 at 0:51
• @maxpax The first two suggestions are ˄E, conjunction elimination. So what conditional(s) are there to be eliminated? What two derivations could result? Jun 6, 2019 at 1:32
• Thank you graham! It's all figured out!
– user39869
Jun 6, 2019 at 2:06