Results 1 to 6 of 6

Math Help - A simple logic problem

  1. #1
    Ant
    Ant is offline
    Member
    Joined
    Apr 2008
    Posts
    140
    Thanks
    4

    A simple logic problem

    Hi,

    If X^2 >= 100 then it follows that X >= 10 or X<= 0. Is this statement true?

    I'm aware that it would certainly be true if the second part was X>= 10 or X<= -10. But I suppose as X<= 0 is more general that X<= -10 (X<=-10 is a subset of X<=0) then it holds as being correct.

    I am right in thinking this?

    Sorry if this is in the incorrect sub forum...

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Ant View Post
    Hi,

    If X^2 >= 100 then it follows that X >= 10 or X<= 0. Is this statement true?

    I'm aware that it would certainly be true if the second part was X>= 10 or X<= -10. But I suppose as X<= 0 is more general that X<= -10 (X<=-10 is a subset of X<=0) then it holds as being correct.

    I am right in thinking this?

    Sorry if this is in the incorrect sub forum...

    Thanks!

    Precisely because it is more general it isn't true: take x=-1<0 . This number fulfills your condition, but x^2=1\ngeq 10 ...

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Ant
    Ant is offline
    Member
    Joined
    Apr 2008
    Posts
    140
    Thanks
    4
    Thanks for your response, I can quite see that your counter example works well. But it's still giving me some trouble.

    If the statement was reduced further to:

    X^2 >= 100 then it follows that X>= 0 or X<= 0.

    Can't the above statement be summarized by saying 'if X squared is greater or equal to 100 then the X is either a positive number of a negative number or it is zero. This is true is it not?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Ant View Post
    Thanks for your response, I can quite see that your counter example works well. But it's still giving me some trouble.

    If the statement was reduced further to:

    X^2 >= 100 then it follows that X>= 0 or X<= 0.

    Can't the above statement be summarized by saying 'if X squared is greater or equal to 100 then the X is either a positive number of a negative number or it is zero. This is true is it not?


    I think I'm beginning to get your logic, and thus I should also change my previous answer: yes, it is true.

    Of course, it is understood that we're talking of real numbers here...

    The other way around, though, is not true.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Of course, it is understood that we're talking of real numbers here...
    Is OP question can be asked when x in C(complex)? (hmmm...)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Ant
    Ant is offline
    Member
    Joined
    Apr 2008
    Posts
    140
    Thanks
    4
    Quote Originally Posted by tonio View Post
    I think I'm beginning to get your logic, and thus I should also change my previous answer: yes, it is true.

    Of course, it is understood that we're talking of real numbers here...

    The other way around, though, is not true.

    Tonio
    Yes, sorry, I probably should have stated that. It is given that X is an element of the set of real numbers.

    Thanks for your responses.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stuck on a simple logic simplification
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: October 27th 2010, 05:20 PM
  2. Simple Percentage Logic
    Posted in the Math Puzzles Forum
    Replies: 11
    Last Post: September 29th 2010, 01:52 PM
  3. simple logic
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: May 13th 2009, 04:13 AM
  4. A simple SD Logic problem that is giving me fits
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 12th 2009, 03:27 PM
  5. A very annoying and simple logic derivation problem.
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: January 14th 2009, 09:01 PM

Search Tags


/mathhelpforum @mathhelpforum