2

I am working on a predicate logic proof given the following premises:

(For all x)(Fx > Vx)

(There exists x)(Fx & Bx)

Desired conclusion: (There exists) (Vx & Bx)

My instinct here says to use universal elimination on the first premise, generate Vx & Bx as a line, and then use existential introduction to finish it off. Any thoughts on how to approach this? I've done the following so far. Apologies for the poor formatting - I am assuming Fw in line 3.enter image description here

1

Using Kevin Klement's natural deduction proof editor and checker here is one solution:

enter image description here

I started with a subproof for existential elimination and then within that subproof used universal elimination. This allowed me to choose the name, "w", in line 3 for existential elimination and use that same name in line 6 for universal elimination.

For more discussion see chapter 32 of P. D. Magnus, Tim Button, J. Robert Loftis, Aaron Thomas-Bolduc, Richard Zach forall x: Calgary Remix.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.