Hey there! Sign in to join this conversationNew here? Join for free
 You are Here: Home >< Maths

# Set theory (cartesian products) - What is wrong with this proof? Watch

1. Status: Problem not yet solved, any help appreciated! (+rep)

(A × B) (C × D) (A C) × (B D)

Notice that above we do not have equality, but containment. What is wrong
with the following attempt at proving the containment the other way round?
Incorrect Theorem. For sets A, B, C, and D we have (A C) × (B D) (A × B) (C × D).
“Proof”. Suppose (x, y) (A C) × (B D). Then x A C and y B D,
so either x A or x C, and either y B or y D. We consider these two cases
separately.
Case 1. x A and y B. Then (x, y) A × B.
Case 2. x C and y D. Then (x, y) C × D.
Thus either (x, y) (A×B) or (x, y) C ×D, so (x, y) (A×B)(C ×D).
The question prior to this one was to prove the containment the 'right' way round which wasn't too hard, but I can't spot what's wrong with this proof, or how to explain it in words, so any hints or help is welcome, still got plenty of rep to give out today and thanks in advance for any help.
2. ... see the thread you posted with the original question
3. (Original post by DeanK22)
... see the thread you posted with the original question
from looking at the other thread i can see generally why the containment doesn't work the other way round from the explanations given by you and ttony, but i cant see how to identify/word whats wrong with this false proof given
4. Neg?
5. (Original post by Lewk)
...
There aren't 2 cases to consider, there are 4.

One is:

Spoiler:
Show

x in A, y in D

6. (Original post by DeanK22)
Neg?
it wasn't me i've already repped you in a post yesterday :

& thanks ghostwalker ill go check that out

Reply
Submit reply
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 10, 2010
Today on TSR

### Oxford grad sues for £1m

Claims damages because he didn't get a first

### 'No evidence of shots fired' at Oxford Circus

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.