| Tired of seeing ads? Click here to upgrade to Elite Membership! |
Mathematics Forum
|
| Author | Message / Information |
| donte Quote | Reply | | SET Theory posted on: 7/29/2006 1:35:41 AM The question is If A U B is a subset of A intersect B, then prove that A=B Now i can see this in my head and it makes sense that the elements in set A and Set B would have to be the same. The problem that i have with subset questions is how to prove that this is the case. I can start by saying For all x ( x is an element of (A U B) --> x is an element of (A intersect B)) ( x is an element of (A U B) --> x is an element of A AND B)) ( x is an element of (A U B) --> x is an element of A AND x is an element of B)) Where do i go from here??? Any help would be great |
|
contrapositive
Quote | Reply | |
SET Theory
replied on: 8/25/2006 3:11:38 AM You can show equality of sets by showing A is a subset of B and B is a subset of A. It's kind of like showing x is less then or equal to y and y is less then or equal to x, the only logical conclusion is x = y. On to the proof: Take any arbitary element of the set A and call it 'a'. Because a is an element of A, a is an element of A OR B. By the definition, a being an element of A OR B means a is also a member of A AND B. If a is in A AND b then a must be an element of B. Thus, all elements in A are in B. Thus, A is a subset of B. You can do the same sort of thing to show B is a subset of A. Thus, A is a subset of B and B is a subset of A, or A = B. |
|
LinkBot
|
Gamers Wanted is looking for people to write game reviews and post news, |
|
|
| Tired of seeing ads? Click here to upgrade to Elite Membership! |
ChatArea.com Help & News Forums | Terms of Use | Contact ChatArea.com | Advertising
Powered By ChatArea.com - Get your free Society today! © Copyright 2003 Wewp!