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

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Homework Help Overview

The discussion revolves around proving the equality (A U B) x (A U B) = (A x A) U (B x B) within the context of discrete mathematics, specifically under the conditions that either A is a subset of B or B is a subset of A.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to prove both sides of the equation, starting with the case where A is a subset of B. They express uncertainty about the implications of this assumption on the equality of the two sides.

Discussion Status

Participants are engaging in an exploratory discussion, with the original poster seeking advice on their reasoning and the validity of their steps. There is an ongoing request for ideas and further input from others.

Contextual Notes

The discussion includes references to specific subset conditions (A C B or B C A) that are central to the proof being attempted. There is also mention of guidelines that participants are expected to follow regarding the presentation of their work.

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

are there any ideas ?

Please Advice,
Dimitry Haritonov
 

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