# Cross Product Problem

• Sep 21st 2012, 12:08 PM
orly11
Cross Product Problem
Hello, i am trying to solve a problem of discrete math and i am having a lot of problem with it(Headbang). 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!!
• Sep 21st 2012, 12:36 PM
Plato
Re: Cross Product Problem
Quote:

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.
• Sep 23rd 2012, 12:05 PM
orly11
Re: Cross Product Problem
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
• Sep 23rd 2012, 12:34 PM
Plato
Re: Cross Product Problem
Quote:

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.
• Sep 23rd 2012, 01:18 PM
orly11
Re: Cross Product Problem
thanks a lot for ur help