Results 1 to 2 of 2

Math Help - binary operation

  1. #1
    Super Member
    Joined
    Aug 2009
    Posts
    639

    binary operation

    For each binary operation * defined, determine whether * is commutative and / or associative.

    (a) on Z, define * by a*b = a-b
    (b) on Q, define * by a*b=ab + 1
    (c) on Z+, define * by a*b= 2^ab

    The answers stated in my notes are
    (a) not comm and not associative
    (b) comm, not associative
    (c) comm, not associative

    Can someone care to explain to me the method to deduce the answers?
    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157
    For commutative you have to check whether:

    a*b = b*a
    a - b \ne b - a

    In this case, it's not closed under commutative.

    For associative you have to check whether:

    (a*b)*c = a*(b*c)
    (a - b)*c = a*(b - c)
    a - b - c = a - (b - c)
    a - b - c = a - b + c

    In this case, it's not closed under associative either.

    Try the next two by yourself, and let me know how they come out.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. binary operation on a set
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: June 16th 2012, 09:12 PM
  2. Binary Operation
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: August 4th 2010, 10:39 AM
  3. New Binary operation
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 16th 2009, 12:31 AM
  4. I Need a Binary Operation
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 8th 2008, 09:14 AM
  5. binary operation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 4th 2008, 02:48 PM

Search Tags


/mathhelpforum @mathhelpforum