Results 1 to 5 of 5

Math Help - Proof without known theorems =/

  1. #1
    Banned
    Joined
    Oct 2009
    Posts
    39
    Thanks
    1

    Proof without known theorems =/

    Hello ppl,

    i am a bit struggling here, i ve been asked to to prove these (below) without using any known theorems , how am i supposed to do that ? any1 knows? Help!

    (a) d |− 流 → d
    (b) {d, 查}|− y (you can use (a)).
    (c) 洵d |- ((查 → 查) → d)


    my nerves, ah .
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    39
    Thanks
    1
    Update:

    i can use these :
    1) d->(y->d)
    2) (d->(y->χ))->((d->y)->(d->χ))
    3) (查-> 流)->((查->y)->d)

    and Modus Ponens..

    any1 ? pls
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,513
    Thanks
    769
    (a) is pretty simple; the length of the shortest derivation is 3.

    (b): from (a), you have 查 |− 流 → 查 and d |− 流 → d. Now use axiom 3 (where d and y are switched).

    (c): again, the formula right of |- seems like the end of axiom 3 where y is 查. This means the beginning of this instance of axiom 3 is 查 -> 洵d. This is derivable from 洵d by (a).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    39
    Thanks
    1
    could some1 please be more analytical, i cant exactly understand what are you trying to tell me there =/
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,513
    Thanks
    769
    For (a), there exists a derivation consisting of 3 formulas. One of them has to be the assumption d. The second has to be an axiom. Then the third is obtained from the first two by MP.

    For the rest, please describe what exactly you don't understand. For example, a hint for (b) says, "from (a), you have 查 |− 流 → 查". Surely you understand that if you take a derivation of d |− 流 → d from (a) and replace d with 查, you get a derivation of 查 |− 流 → 查.

    As a general remark, I would not try solving this problem without first studying several examples of derivations from the textbook or lecture notes. You need to understand how this calculus works and have some intuition about it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Egoroff's Theorems Proof
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: November 23rd 2011, 11:20 PM
  2. Proof of Theorems
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 26th 2009, 04:08 AM
  3. Proof by using multiple theorems
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: January 23rd 2008, 04:26 AM
  4. Theorems
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 4th 2007, 08:03 PM
  5. Theorems
    Posted in the Algebra Forum
    Replies: 5
    Last Post: July 15th 2006, 08:43 AM

Search Tags


/mathhelpforum @mathhelpforum