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Math Help - Set Prove or Disprove

  1. #1
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    Set Prove or Disprove

    Last help i need for today

    Prove or Disprove:

    (A multiply C) Union (B multiply D) = (A Intersection B) multiply (C Intersection D).

    Please help...

    When multiply is coming in SET, my brain is not working
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  2. #2
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    Did you mean: (A\times C) \cup  (B \times D) = (A \cap B) \times (C \cap D) ?

    If so, then you should note that:

    X \times Y = \left\{(x,y) : x \in X; y \in Y\right\} for any two sets X,Y. Once this is clear, this should be easy to solve!
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  3. #3
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    Quote Originally Posted by faisalnet5 View Post
    Prove or Disprove:
    (A multiply C) Union (B multiply D) = (A Intersection B) multiply (C Intersection D).
    You are asked Prove or Disprove: \left( {A \times C} \right) \cup \left( {B \times D} \right) = \left( {A \cap B} \right) \times \left( {C \cap D} \right)

    First, \left( {A \times C} \right) is read "A cross C"; not (A multiply C)
    It is the cross product of set A with set C.
    A = \left\{ {1,2} \right\}\;\& \;C = \left\{ {2,3} \right\}\; \Rightarrow \;\left( {A \times C} \right) = \left\{ {\left( {1,2} \right),\left( {1,3} \right),\left( {2,2} \right),\left( {2,3} \right)} \right\}.

    Now if B = \left\{ 4 \right\}\;\& \;D = \left\{ 5 \right\} is it true?
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  4. #4
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    Thanks a lot Plato...u know i am new in this room and yet don't know how to use the signs like u did. Will be on the road soon

    By the way, so if someone ask me to prove :

    \left( {A \times C} \right) \cup \left( {B \times D} \right) = \left( {A \cap B} \right) \times \left( {C \cap D} \right)

    Do i have to take some arbitrary sets like that A={1,2}, C={2,3}...and solve it or by using set notation also we can prove or disprove?

    Regards
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  5. #5
    ynj
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    Quote Originally Posted by faisalnet5 View Post
    Thanks a lot Plato...u know i am new in this room and yet don't know how to use the signs like u did. Will be on the road soon

    By the way, so if someone ask me to prove :

    \left( {A \times C} \right) \cup \left( {B \times D} \right) = \left( {A \cap B} \right) \times \left( {C \cap D} \right)

    Do i have to take some arbitrary sets like that A={1,2}, C={2,3}...and solve it or by using set notation also we can prove or disprove?

    Regards
    not exactly. Often we use algebraic method or deduction,
    like A\cap (B\cup C)=(A\cap B)\cup (A\cap C)or "if A is in B, then ...."..
    But this is used to prove something. If you want to disprove, just give a conterexample.
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