Results 1 to 2 of 2

Math Help - Which relations are reflexive

  1. #1
    Newbie
    Joined
    Aug 2012
    From
    america
    Posts
    1

    Which relations are reflexive

    Which of the following relations are reflexive

    1) x~y if and only if x-y is a multiple of 10
    2) x~y if and only if xy >= 0
    3) x~y if and only if x - y is positive
    4) x~y if and only if x+y is odd
    5) x~y if and only if x+y is positive

    I know the definition of reflexixe is xRx but i dont really understand how to apply it

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,540
    Thanks
    780

    Re: Which relations are reflexive

    Well, let's start from the beginning. First, you need to know how to substitute a concrete expression for a variable in another expression. Here are a few exercises. Please write the answers.

    (1) Substitute 2 for x (i.e., replace x with 2) in x + 2 = 4.
    (2) Substitute (3 + 5) for y in (y + 1) = y + 2y + 1. Don't do any simplification; just do the substitution.
    (3) Let the function f(x) be defines as x + 1. Replace f with its definition in f(y + 2) + f(y + 3) = 2y + 7. Again, don't do any simplification.
    (4) Let the relation R(x,y) be defines as x < y and let U(x,y) be defined as x ≤ y. Replace R and U with their definitions in "R(x,y + 1) if and only if U(x,y)."

    Second, you need correct definitions.

    Quote Originally Posted by hampsterbones View Post
    I know the definition of reflexixe is xRx
    This resembles the correct definition, but it's so sloppy that it's not a definition at all. Write the correct, precise definition of "reflexive." Be sure to consult the source (textbook or lecture notes). The definition should start with "A binary relation R on a set A is reflexive if ..." Note that your original question lacks some information because it does not say on which set we consider those relations.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Total no. of reflexive relations on a set of n elements
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: December 29th 2011, 01:24 AM
  2. Replies: 1
    Last Post: September 19th 2011, 01:09 PM
  3. Relations, reflexive and transitive
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: October 5th 2010, 02:36 AM
  4. reflexive in relations
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 27th 2008, 03:41 PM
  5. Reflexive relations proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 14th 2007, 03:46 AM

Search Tags


/mathhelpforum @mathhelpforum