# I need help to Derive F & G

Derive F & G

1. F=G. Assump.

2. F v G. Assump.

? G.

F & G. & I 1-?

Should l use disjunction elimination or biconditional elim. next? I am flubbered

Help

• Maybe you should try both and then try to understand the reasons for success and failure? That's how you learn the most. – Philip Klöcking Mar 7 at 17:18
• I tried disjunction say let’s try disjunction F (assump) | G 2 V elimin. G(assump)|G 2 V eliminate. Sorry for poor formatting. – larry mintz Mar 7 at 17:44
• I’m voting to close this question because forum is not a logic homework help site. – Swami Vishwananda Mar 8 at 4:23
• I solved it. Plus it is not a homework problem. I am bored and doing it for fun – larry mintz Mar 8 at 13:20
• Although the problem is probably trivial, I have no idea what you're asking here. Derive G from F & G? And in what kind of deduction system? – Fizz Mar 9 at 14:56

Disjunction Elimination has a "Proof by Cases" structure.

``````m.|  A v B
n.|  |_ A
|  |  :
o.|  |  C
|  +
p.|  |_ B
|  |  :
q.|  |  C
|  C            vE m,n-o,p-q
``````

Biconditional Elimination .. has various presentations, but basically

``````m.|   A = B
n.|   A
|   B          =E m,n
``````

or perhaps it eliminates to the conditionals so...

``````m.|  A = B
n.|  A
o.|  A > B      =E m
|  B          >E o,n
``````

Check how your particular version operates.

But basically your proof will be a Disjunction Elimination, whose subproof for each case shall contain a Biconditional Elimination and Conjunction Introduction.

The later being of the form:

``````  m.|  A
n.|  B
|  A & B   &I m,n
``````

Like so...

`````` 1.|  F = G        Premise
2.|_ F v G        Premise
3.|  |_ F         Assume
|  |  :
|  |  G         via =E however it works
|  |  F & G     &I 3, ?
|  +
|  |_ G         Assume
|  |  :
|  |  F & G     Somehow
|  F & G        vE 2, 3-?, ?-?
``````

Just fill in the missing details.

• Where could l get a good version of Fitch – larry mintz Mar 13 at 16:54