I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : [![enter image description here]] 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?
closed as unclear what you're asking by Graham Kemp, Joseph Weissman♦ Jun 6 at 3:00
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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