Results 1 to 2 of 2

Math Help - Relations with

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    23

    Relations with

    Let A=, and consider the empty relation, , on A. Which properties does satisfy?

    Is it reflexive, irreflexive, symmetric, antisymmetric, transitive?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,545
    Thanks
    1394
    Quote Originally Posted by kturf View Post
    Let A=, and consider the empty relation, , on A. Which properties does satisfy?

    Is it reflexive, irreflexive, symmetric, antisymmetric, transitive?
    Use the fact that if p is false, then the statement "if p then q" is true no matter what q is.

    "reflexive" means "if x is in A, then (x,x) is in the relation". But, since A is empty, "x is in A" is false for all x.

    "irreflexive" means "if x is in A, then (x,x) is NOT in the relation". But, since A is empty, "x is in A" is false for all x.

    "Symmetric' means "if (x,y) is in the relation then (y,x) is in the relation". But, since is the empty relation, "(x,y) is in the relation" is false for all x, y.

    "Anti-symmetric" means "if (x,y) is in the relation then (y,x) is NOT in the relation. But, since is the empty relation "(x,y) is in the relation" is false for all x,y.

    "transitive" means "if (x,y) and (y,z) are in the relation then (x,z) is in the relation". But, since is the empty relation, "(x,y) and (y,z) are in the relation" is false for all x,y,z.

    Once again, if the hypothesis, p, of the statement "if p then q" is false the statement itself is true.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Relations and Functions - Inverse Relations Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 13th 2011, 12:20 PM
  2. Replies: 1
    Last Post: September 19th 2011, 01:09 PM
  3. [SOLVED] Relations on A
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: November 21st 2010, 11:25 AM
  4. Relations in a set
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 5th 2010, 10:03 PM
  5. relations help (3)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 18th 2010, 04:49 AM

Search Tags


/mathhelpforum @mathhelpforum