Results 1 to 3 of 3

Math Help - Research Help

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    6

    Research Help

    I need some help , i doing my in formal methods (formal verification) i am facing a problem and need an expert opinion i have set say {s | f + g = k} where f and g are some functions
    and k is number i want to split this set into two set (union or intersection) as {s | f = i} union (or intersection) {s | g = j} , first i want to ask can i do it , secondly what will be values of i & j (with respect to k), looking forward for some body who can help me out...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,517
    Thanks
    771
    Clearly, for any i, j such that i + j = k, we have

    \{x\mid f(x)=i\}\cap\{x\mid g(x)=j\}\subset\{x\mid f(x)+g(x)=k\}.

    However, the converse inclusion does not hold because the fact that f(x) + g(x) = k does not uniquely determine f(x) and g(x). The only thing that comes to mind when i, j and k are natural numbers is

    \bigcup_{i=0}^k\{x\mid f(x)=i\}\cap\{x\mid g(x)=k-i\}=\{x\mid f(x)+g(x)=k\}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    Posts
    6
    Thanks for answering my post
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Research
    Posted in the Statistics Forum
    Replies: 3
    Last Post: May 30th 2011, 03:49 AM
  2. Operations Research
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: February 19th 2010, 07:52 AM
  3. Research Analysis
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 6th 2009, 03:56 PM
  4. Just Research...........
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: June 5th 2008, 04:29 AM
  5. Need help for research analysis
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 8th 2007, 08:30 PM

Search Tags


/mathhelpforum @mathhelpforum