Results 1 to 8 of 8

Math Help - Is this correct? (It deals with A x B x C stuff)

  1. #1
    Member
    Joined
    Jan 2009
    Posts
    93

    Is this correct? (It deals with A x B x C stuff)

    Q: Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find:
    a.) A x B x C
    b.) C x B x A
    c.) C x A x B
    d.) B x B x B

    a.) A x B x C = [{a, x, 0}, {a, y, 1}, {b, x, 0}, {b, y, 1}, {c, x, 0}, {c, y, 1}]
    b.) C x B x A = [{0, x, a}, {0, x, b}, {0, x, c}, {1, y, a}, {1, y, b}, {1, y, c}]
    c.) C x A x B = [{0, a, x}, {0, b, x}, {0, c, x}, {1, a, y}, {1, b, y}, {1, c, y}]
    d.) B x B x B = [{x, x, x}, {x, x, y}, {x, y, x}, {y, y, y}, {y, y, x}, {y, x, y}]

    __________
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by Grillakis View Post
    Q: Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find:
    a.) A x B x C
    b.) C x B x A
    c.) C x A x B
    d.) B x B x B

    a.) A x B x C = [{a, x, 0}, {a, y, 1}, {b, x, 0}, {b, y, 1}, {c, x, 0}, {c, y, 1}]
    b.) C x B x A = [{0, x, a}, {0, x, b}, {0, x, c}, {1, y, a}, {1, y, b}, {1, y, c}]
    c.) C x A x B = [{0, a, x}, {0, b, x}, {0, c, x}, {1, a, y}, {1, b, y}, {1, c, y}]
    d.) B x B x B = [{x, x, x}, {x, x, y}, {x, y, x}, {y, y, y}, {y, y, x}, {y, x, y}]

    __________
    Well a isn't right.

     A \times B \times C = \bigg\{(f,g,h) | f \in A, g \in B, h \in C\bigg\}

    Now, I see no element (a,x,1) in your first set, and that satisfies the conditions. You are correct with what you have, but just not complete.
    Last edited by Mush; February 6th 2009 at 05:57 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2009
    Posts
    93
    Quote Originally Posted by Mush View Post
    Well a isn't right.

     A \times B \times C = \bigg{(f,g,h) | f \in A, g \in B, h \in C\bigg}

    Now, I see no element (a,x,1) in your first set, and that satisfies the conditions. You are correct with what you have, but just not complete.
    How about now Mush ( is everything correct now):

    A x B x C = [{a, x, 0}, {a, x, 1}, {a, y, 0}, {a, y, 1}, {b, x, 0}, {b, x, 1},
    {b, y, 0}, {b, y, 1}, {c, x, 0},
    {c, x, 1}, {c, y, 0}, {c, y, 1}]

    C x B x A = [{0, x, a}, {0, x, b}, {0, x, c}, {1, y, a}, {1, y, b}, {1, y, c}]

    C x A x B = [{0, a, x}, {0, b, x}, {0, c, x}, {1, a, y}, {1, b, y}, {1, c, y}]

    B x B x B = [{x, x, x}, {x, x, y}, {x, y, x}, {y, y, y}, {y, y, x}, {y, x, y}]

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by Grillakis View Post
    How about now Mush ( is everything correct now):

    A x B x C = [{a, x, 0}, {a, x, 1}, {a, y, 0}, {a, y, 1}, {b, x, 0}, {b, x, 1},
    {b, y, 0}, {b, y, 1}, {c, x, 0},
    {c, x, 1}, {c, y, 0}, {c, y, 1}]

    C x B x A = [{0, x, a}, {0, x, b}, {0, x, c}, {1, y, a}, {1, y, b}, {1, y, c}]

    C x A x B = [{0, a, x}, {0, b, x}, {0, c, x}, {1, a, y}, {1, b, y}, {1, c, y}]

    B x B x B = [{x, x, x}, {x, x, y}, {x, y, x}, {y, y, y}, {y, y, x}, {y, x, y}]
    a) is now complete.
    b) is not complete, for example, (1,x,c) is not there.
    c) is not complete, for example, (0,a,y) is not there.
    d) is not complete, for example, (x,y,y) is not there.

    Hint: a), b) and c) should have the same number of elements. d) should have 8 elements.

    PS your notation is wrong. Your sets A x B x C should be sets of ordered-3tuples, not sets of sets! Curly brackets denote sets, normal brackets denote ordered n-tuples:

    a) should be:

     A \times B \times C = \bigg\{(a, x, 0), (a, x, 1), (a, y, 0), (a, y, 1), (b, x, 0),  (b, x, 1), <br />
                    (b, y, 0), (b, y, 1), (c, x, 0),(c, x, 1), (c, y, 0), (c, y, 1)\bigg\}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2009
    Posts
    93
    Quote Originally Posted by Mush View Post
    a) is now complete.
    b) is not complete, for example, (1,x,c) is not there.
    c) is not complete, for example, (0,a,y) is not there.
    d) is not complete, for example, (x,y,y) is not there.

    Hint: a), b) and c) should have the same number of elements. d) should have 8 elements.

    PS your notation is wrong. Your sets A x B x C should be sets of ordered-3tuples, not sets of sets! Curly brackets denote sets, normal brackets denote ordered n-tuples:

    a) should be:

     A \times B \times C = \bigg\{(a, x, 0), (a, x, 1), (a, y, 0), (a, y, 1), (b, x, 0),  (b, x, 1), <br />
                    (b, y, 0), (b, y, 1), (c, x, 0),(c, x, 1), (c, y, 0), (c, y, 1)\bigg\}
    Mush, hopefully 3rd times a charm:

    A x B x C = {(a, x, 0), (a, x, 1), (a, y, 0), (a, y, 1), (b, x, 0), (b, x, 1), (b, y, 0),
    (b, y, 1), (c, x, 0),
    (c, x, 1), (c, y, 0), (c, y, 1)}

    C x B x A = {(0, x, a), (0, x, b), (0, x, c), (1, x, a), (1, x, b), (1, x, c), (0, y, a),

    (0, y, b), (0, y, c), (1, y, a), (1, y, b), (1, y, c)}

    C x A x B = {(0, a, x), (0, b, x), (0, c, x), (1, a, x), (1, b, x), (1, c, x), (0, a, y),
    (0, b, y), (0, c, y),
    (1, a, y), (1, b, y), (1, c, y)}

    B x B x B = {(x, x, x), (x, x, y), (x, y, x), (x, y, y), (y, y, y), (y, y, x), (y, x, y),
    (y, y, x)}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by Grillakis View Post
    Mush, hopefully 3rd times a charm:

    A x B x C = {(a, x, 0), (a, x, 1), (a, y, 0), (a, y, 1), (b, x, 0), (b, x, 1), (b, y, 0),
    (b, y, 1), (c, x, 0),
    (c, x, 1), (c, y, 0), (c, y, 1)}

    C x B x A = {(0, x, a), (0, x, b), (0, x, c), (1, x, a), (1, x, b), (1, x, c), (0, y, a),

    (0, y, b), (0, y, c), (1, y, a), (1, y, b), (1, y, c)}

    C x A x B = {(0, a, x), (0, b, x), (0, c, x), (1, a, x), (1, b, x), (1, c, x), (0, a, y),
    (0, b, y), (0, c, y),
    (1, a, y), (1, b, y), (1, c, y)}

    B x B x B = {(x, x, x), (x, x, y), (x, y, x), (x, y, y), (y, y, y), (y, y, x), (y, x, y),
    (y, y, x)}
    You put (y,y,x) in twice on the last one, and missed out (y,x,x). Apart from that, it's perfect.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Jan 2009
    Posts
    93
    Quote Originally Posted by Mush View Post
    You put (y,y,x) in twice on the last one, and missed out (y,x,x). Apart from that, it's perfect.
    lol...thanks mush
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    The first thing you should have thought: Since A has 3 members and B and C both have 2, A X B X C, B X C X A, and C X A X B will have 3(2)(2)= 12 members while B X B X B will have 2(2)(2)= 8 members.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 15
    Last Post: July 29th 2011, 01:39 AM
  2. kid stuff
    Posted in the Math Puzzles Forum
    Replies: 9
    Last Post: September 8th 2009, 08:24 AM
  3. More log stuff
    Posted in the Math Topics Forum
    Replies: 18
    Last Post: May 12th 2008, 07:24 PM
  4. Need help with ln and e stuff
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2008, 05:05 PM
  5. deals of n cards for all cards appear once
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 7th 2007, 07:26 AM

Search Tags


/mathhelpforum @mathhelpforum