Results 1 to 3 of 3

Math Help - 2 simple proof questions, logic related

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    175

    2 simple proof questions, logic related

    1.Suppose x and y are real numbers. Prove or give a counterexample.

    if x + y is irrational, the x is irrational or y is irrational.

    I found a counterexample already in a earlier question that asked if x is irrational and y is irrational, then x + y is irrational, but im not sure how to approach this question.

    2.If x is a real number, then  |x-2| \leq 3 implies that  -1 \leq x \leq 5.

    for this one, im not sure how to deal with the absolute value.
    Thanks
    Last edited by p00ndawg; September 10th 2009 at 07:06 PM. Reason: better title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    May 2009
    Posts
    471
    For the second one, take an alternative definition of absolute value,

    |x|= \sqrt{x^2} then the equation is easily solved as long as you remember to take both positive and negative square root when the time comes
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    May 2009
    Posts
    471
    prove the first one by proving the contrapostive and use the fact that the sum of two rational numbers is a rational number (easiest to see if you use fractions and remember that all the variables are integers)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] logic related question ...
    Posted in the Discrete Math Forum
    Replies: 41
    Last Post: July 11th 2011, 05:28 AM
  2. Simple logic proof, need help interpreting
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: January 25th 2011, 01:14 PM
  3. Proof System questions (Logic)
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 21st 2009, 07:50 PM
  4. Some Simple Predicate Logic Questions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 24th 2009, 08:22 AM
  5. simple logic
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: May 13th 2009, 03:13 AM

Search Tags


/mathhelpforum @mathhelpforum