Cross Product Problem

**orly11** · September 21st 2012, 12:08 PM

Hello, i am trying to solve a problem of discrete math and i am having a lot of problem with it

. if someone could help me please

The exercise is the following:

If A,B,C are sets, then show that

A X (B U C) = (A X B) U (A X C)

Thanks!!

**Plato** · September 21st 2012, 12:36 PM

Originally Posted by orly11

Hello, i am trying to solve a problem of discrete math and i am having a lot of problem with it. if someone could help me please The exercise is the following:
If A,B,C are sets, then show that
A X (B U C) = (A X B) U (A X C)

The statement that $(x,y)\in A\times (B\cup C)$ means that $x\in A~\&~y\in (B\cup C)$ .

The statement that $(x,y)\in[( A\times B)\cup(A\times C)]$ means that $(x,y)\in(A\times B)\text{ or }(x,y)\in(A\times C)$ .

Now you show those to are equivalent.

**orly11** · September 23rd 2012, 12:05 PM

I am having trouble showing that their are equivalent. I have 3 more exersice like this one, can u help me with the prove so that I can take this exercise as an example
Thanks for your help

**Plato** · September 23rd 2012, 12:34 PM

Originally Posted by orly11

I am having trouble showing that their are equivalent. I have 3 more exersice like this one, can u help me with the prove so that I can take this exercise as an example

Here is the proof: $(x \in A) \wedge \left[ {y \in B \vee y \in C} \right] \Leftrightarrow \left[ {\left( {x \in A \wedge y \in B} \right) \vee \left( {x \in A \wedge y \in C} \right)} \right]$ .

If you know the meaning of cross product and you read my first reply, then it should be clear to you.

**orly11** · September 23rd 2012, 01:18 PM

thanks a lot for ur help

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