Solve the following proof : M |- M ∨ {[(Z∨S) ∧ (¬] → (C↔D)}

Question

Solve the following proof :

M |- M ∨ {[(Z∨SC↔D)}

I try to proof above question with the following

1. (F⋀Z)⋀ → (C↔D)

   1 (F⋀Z)→C

   2 F⋀Z 1⋀E

   3 F 2⋀E

really confused :(

this examples

Answer 1

What do you mean by "solve"?

If to "solve" something of the form $A \vdash B$ means "produce a proof in the formal proof system in My Logic Text from premiss $A$ to $B$" (which is the natural reading) then we need to know which text you are using!

In this case you have $M \vdash M \lor X$. And it doesn't matter what $X$ is, for in any standard logical proof system you can prove $M \lor X$ from $M$ (for any $X$). But how the proof goes will depend on the chosen proof system.

If you are using a natural deduction system, then there will be a basic two-part rule "from $A$ you can infer $A \lor B$, and from $A$ you can infer $B \lor A$ for any $B$". So your claim has a one-step proof invoking the first part of this rule!

In a Hilbert-style proof system, more work will be needed: what work will depend on the details of Your Logic Text.

[If you mean something else by "solve", then you need to tell us, as you aren't using the word in a standard sense in this context.]