Results 1 to 3 of 3

Math Help - Associativity Proof

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    37

    Associativity Proof

    Prove or disprove in set \mathbb{R} defined algebraic operation \circ associativity if:

    x\circ y = xy - x - y +2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    614
    Hello, Bernice!

    Prove or disprove in set \mathbb{R} defined algebraic operation \circ associativity if:

    x\circ y \:= \:xy - x - y +2
    I find that it helps to use baby-talk . . .

    x \circ y \:\text{ means: }\:\begin{Bmatrix}\text{multiply the two terms,}\\ \text{minus the first term,} \\ \text{minus the second term,} \\ \text{then add 2.} \end{Bmatrix}


    We will see if: . (a \circ b)\circ c \:=\: a\circ(b\circ c)


    . . . a\circ b \;=\;ab - a - b + 2

    (a\circ b)\circ c \;=\; (ab - a - b + 2)\circ c

    . . . . . . =\; (ab-a-b+2)c - (ab-a-b+2) - c + 2

    . . . . . . =\; abc - ac - bc + 2c - ab + a + b - 2 - c + 2

    . . . . . . =\; {\color{blue}abc - ab - bc - ac + a + b + c}



    . . . (b\circ c) \;=\;bc - b - c + 2

    a\circ(b\circ c) \;=\;a\circ(bc - b - c + 2)

    . . . . . . = \;a(bc-b-c+2) - a - (bc-b-c+2) + 2

    . . . . . . =\; abc - ab - ac + 2a - a - bc + b + c - 2 + 2

    . . . . . . =\; {\color{blue}abc - ab - bc - ac + a + b + c}



    They are equal! . . . (a\circ b)\circ c \;=\;a\circ(b\circ c)

    Therefore, the operation is associative.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Beat to it. Nevermind.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: April 26th 2011, 01:58 PM
  2. Cross product - associativity
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 22nd 2011, 01:04 AM
  3. Replies: 5
    Last Post: October 19th 2010, 10:50 AM
  4. associativity
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 21st 2010, 11:29 AM
  5. Replies: 2
    Last Post: May 29th 2009, 01:47 PM

Search Tags


/mathhelpforum @mathhelpforum