Results 1 to 3 of 3

Math Help - Commutative and Associative 71.5

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    62

    Commutative and Associative 71.5

    Define the operation ^on Z by x^y= the smaller of x and y. For example 2^5=2, 3^-4=-4, 4^4= 4. Answer the following questions and justify your answers.

    a. Is this operation commutative?
    b. Is this operation associative?
    c. Does this operation have an identity in Z?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by tigergirl View Post
    Define the operation ^on Z by x^y= the smaller of x and y. For example 2^5=2, 3^-4=-4, 4^4= 4. Answer the following questions and justify your answers.

    a. Is this operation commutative?
    b. Is this operation associative?
    c. Does this operation have an identity in Z?
    The operation is commutative since x \wedge y = \min\{x,y\}=\min\{y,x\}=y\wedge x

    The operation is also associative since

    x\wedge (y\wedge z)=x\wedge\min\{y,z\}=\min\{x,\min\{y,z\}\}=\min\{  \min\{x,y\},z\} =\min\{x,y\}\wedge z=(x\wedge y)\wedge z

    I'm not sure what to say with regards to (c). Maybe someone else can jump in and answer that.

    Does everything else make sense?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    To pick up where chris left off. If there were an identity I it would need to satisfy this property

    I^x=x^I=x for all x \in \mathbb{Z}

    what this would imply is that I is larger than every integer.

    i.e I = \infty but infinity is not a number.

    so there is not an identity.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Commutative and Associative properties.
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: June 5th 2012, 05:30 PM
  2. Commutative and Associative relations of binary operations
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: May 15th 2011, 06:39 AM
  3. Replies: 3
    Last Post: December 29th 2009, 04:13 PM
  4. commutative, associative
    Posted in the Algebra Forum
    Replies: 8
    Last Post: October 22nd 2009, 09:52 PM
  5. Prove * is commutative and associative
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 4th 2008, 05:25 PM

Search Tags


/mathhelpforum @mathhelpforum