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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- Aug 31st 2009, 08:41 AMfaisalnet5Set 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 :( - Aug 31st 2009, 09:09 AMDefunkt
Did you mean: $\displaystyle (A\times C) \cup (B \times D) = (A \cap B) \times (C \cap D)$ ?

If so, then you should note that:

$\displaystyle X \times Y = \left\{(x,y) : x \in X; y \in Y\right\}$ for any two sets $\displaystyle X,Y$. Once this is clear, this should be easy to solve! - Aug 31st 2009, 09:10 AMPlato
You are asked Prove or Disprove: $\displaystyle \left( {A \times C} \right) \cup \left( {B \times D} \right) = \left( {A \cap B} \right) \times \left( {C \cap D} \right)$

First, $\displaystyle \left( {A \times C} \right)$ is read "A cross C"; not (A multiply C)

It is the cross product of set A with set C.

$\displaystyle A = \left\{ {1,2} \right\}\;\& \;C = \left\{ {2,3} \right\}\; \Rightarrow \;\left( {A \times C} \right) = \left\{ {\left( {1,2} \right),\left( {1,3} \right),\left( {2,2} \right),\left( {2,3} \right)} \right\}$.

Now if $\displaystyle B = \left\{ 4 \right\}\;\& \;D = \left\{ 5 \right\}$ is it true? - Aug 31st 2009, 09:16 AMfaisalnet5
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 - Sep 1st 2009, 02:08 AMynj