Results 1 to 9 of 9

Math Help - Finding the Converse & Contrapositive of a Statement

  1. #1
    Junior Member
    Joined
    Sep 2008
    From
    Oregon
    Posts
    58

    Finding the Converse & Contrapositive of a Statement

    Hi all,

    I need to find the converse & contrapositive of the following statement:

    "For all positive real numbers x, there exists an integer n such that
    1/n < x."

    Thanx in advance for your help!
    Oh.... and I found the negation of this stmt. to be:

    There is a positive real number x such that for all n, if n is not an integer, then 1/n is greater than or equal to x (I don't know how to use latex).....is this right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Quote Originally Posted by dolphinlover View Post
    There is a positive real number x such that for all n, if n is not an integer, then 1/n is greater than or equal to x (I don't know how to use latex).....is this right?
    Here is the negation.
    \left( {\exists x \in \mathbb{R}^ +  } \right)\left( {\forall n \in \mathbb{N}^ +  } \right)\left[ {\frac{1}{n} \geqslant x} \right]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    From
    Oregon
    Posts
    58
    That is what I have...can you help with the converse and contrapositive?(symbols are fine) I am stuck on that part & I have several more problems that are similar to this one.

    Thank You!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Quote Originally Posted by dolphinlover View Post
    "For all positive real numbers x, there exists an integer n such that
    1/n < x."
    There is a positive real number x such that for all n, if n is not an integer, then 1/n is greater than or equal to x (I don't know how to use latex).....is this right?
    [/QUOTE]

    Quote Originally Posted by dolphinlover View Post
    That is what I have...
    No it is not what you had.
    Look at the text in “red”. That is wrong!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2008
    From
    Oregon
    Posts
    58
    Hi again Plato,

    So your negation in words reads..."There is a positive real number x, s.t. for all positive natural numbers n, 1/n is greater than or equal to x"?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Quote Originally Posted by dolphinlover View Post
    So your negation in words reads..."There is a positive real number x, s.t. for all positive natural numbers n, 1/n is greater than or equal to x"?
    Correct: \neg \left( {\forall x} \right)\left( {\exists y} \right)\left[ {P(x,y)} \right] \equiv \left( {\exists x} \right)\left( {\forall y} \right)\left[ {\neg P(x,y)} \right]

      P \Rightarrow Q\,\mbox{ converse } \,Q \Rightarrow P
      P \Rightarrow Q\,\mbox{ Contrapositive } \,\neg Q \Rightarrow \neg P
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Sep 2008
    From
    Oregon
    Posts
    58

    Arrow

    Symbolically, I understand the converse and contrapositive. The problem I'm having is with the Quantifiers being part of the implication.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Quote Originally Posted by dolphinlover View Post
    The problem I'm having is with the Quantifiers being part of the implication.
    Well translate it into standard English without quantifiers.
    If x is a positive real number then there is a positive integer, n, such that (1/n)<x.

    Now you have P & Q.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Sep 2008
    From
    Oregon
    Posts
    58
    That helps.....Thank You!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. inverse, converse, and contrapositive?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 28th 2011, 05:24 AM
  2. converse & contrapositive
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 28th 2010, 07:49 AM
  3. Converse and Contrapositive
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: October 30th 2009, 10:17 AM
  4. converse and contrapositive
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: December 8th 2008, 09:26 AM
  5. Converse and contrapositive
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 1st 2008, 01:26 PM

Search Tags


/mathhelpforum @mathhelpforum