Results 1 to 2 of 2

Math Help - Need help writing the logical formulation of statements

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    79

    Need help writing the logical formulation of statements

    I am needing some help writing the logical formulation of statements.
    For example, here are some statements:
    1. Between any two real numbers there is at least one rational number and one irrational number.
    2. If r1 and r2 are any real numbers satisfying r1 < r2, then r1+a < r2+a for each real number a.
    3. If a, b, and c are any real numbers, then a(b+c)=ab+ac.

    I think the problem is that my teacher didn't give us any type of examples of doing this, so I am having a hard time figuring them out. I would appreciate any and ALL advice you can give me on doing these. Also, how do you know what the universe is for these things?

    Thank you so much for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,527
    Thanks
    773

    Re: Need help writing the logical formulation of statements

    1. \forall x\in\mathbb{R}\,\forall y\in\mathbb{R}\,\Big(x<y\to\big(\exists u\in\mathbb{Q}\,(x<u\land u<y)\big)\land\big(\exists v\in\mathbb{R}\setminus\mathbb{Q}\,(x<v\land v<y)\big)\Big)

    3. \forall a\in\mathbb{R}\,\forall b\in\mathbb{R}\,\forall c\in\mathbb{R}\,a(b+c)=ab+ac

    Try writing 2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: November 27th 2011, 11:39 AM
  2. [SOLVED] Confused about logical equivalence of some statements
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: July 13th 2011, 04:44 AM
  3. Logical statements
    Posted in the Discrete Math Forum
    Replies: 20
    Last Post: August 17th 2010, 01:55 AM
  4. Prove/disprove using logical using logical arguments
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 24th 2010, 06:29 AM
  5. Replies: 3
    Last Post: January 21st 2010, 07:45 AM

Search Tags


/mathhelpforum @mathhelpforum