# Thread: Set Prove or Disprove

1. ## 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).

When multiply is coming in SET, my brain is not working

2. 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!

3. Originally Posted by faisalnet5
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?

4. 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

5. Originally Posted by faisalnet5
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.