Proving (A U B) x (A U B) = (A x A) U (B x B) with Discrete Math

[sallaboy]

Hello,

How do I proove :

(A U B) x (A U B) = (A x A) U (B x B)

if and only if : (A C B) or (B C A) ?

Please Advice,
Dimitry Haritonov

 

[quantumdude]

Please show what you've done so far, as per the Guidelines you agreed to.

 

[sallaboy]

Dear Tom,

First of all I need to proove the two sides.

so I've started with first side when ACB:

(a,b)E(AUB)x(AUB) => aE(AUB) and bE(AUB) => if ACB so AUB=B => aEB and bEB => (a,b)E(BxB)

the second side:

(a,b)E(AxA)U(BxB) => here I have a little problem, I don't sure that I can to state that: if ACB so (AxA)U(BxB) = (BXB).

If It's right, I can continue:

...(a,b)E(BXB)

and we got the same result by the two sides.

Please Advice,
Dimitry Haritonov

 

[sallaboy]

Dear Tom,

are there any ideas ?

Please Advice,
Dimitry Haritonov