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#1 2007-09-19 14:38:55

MarkusD
Member
Registered: 2006-10-08
Posts: 28

Composite of Two Relations

Hello everyone, I have the following:

S={(4,5),(4,6),(5,4),(6,6)}

What is SoS^-1?

Now I wrote that S^-1={(5,4),(6,4),(4,5),(6,6)}

So I should have:

{(4,4), (4,4), (5,5), (6,6)}

but the back of my book says that I should (5,6) and (6,5) as part of the solution. Can anyone explain?

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#2 2007-09-19 15:35:36

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Composite of Two Relations

5 goes to 4 in S^-1, and 4 goes to both 5 and 6 in S.  So 5 goes to 5 and 5 goes to 6.  The same thing happens with 6.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2007-09-19 16:28:18

MarkusD
Member
Registered: 2006-10-08
Posts: 28

Re: Composite of Two Relations

Ricky wrote:

5 goes to 4 in S^-1, and 4 goes to both 5 and 6 in S.  So 5 goes to 5 and 5 goes to 6.  The same thing happens with 6.

How does that happen. I thought that you take the first elements of S and pair them with the second elements in S^-1. Since there are 4 pairs, you should get 4 pairs at the end right?

Last edited by MarkusD (2007-09-19 16:29:02)

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