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Susan123456
Senior Member
Joined: 18 Jul 2008
Posts: 114
Location: California, USA
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 Posted: Sat, 7 Nov 2009 20:52:53 UTC Post subject: Composition |
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Hello, I was hoping someone could help me with the following problems. I just don't know why I keep getting the wrong answer even though I drew the pictures and the arrows.
Problem Statement: Let R = {(1,5), (2,2), (3,4), (5,2)}, S= {(2,4), (3,4), (3,1), (5,5)} and T={(1,4), (3,5), (4,1)}. Find
a) R 0 S
b) T 0 S
c) R 0 (S 0 T)
Please note that "0" means "composite". Would someone let me know what I should do?
Thank you so much,
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Nona M.
S.O.S. Oldtimer
Joined: 17 Apr 2008
Posts: 201
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| Posted: Mon, 9 Nov 2009 12:47:10 UTC Post subject: |
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To find the set of points for (R o S)(x) = R(S(x)), pick an x-value from S, find the corresponding y-value for S, plug this into R as an x-value, and find the corresponding y-value for R. The x-value for S and the y-value for R are an (x,y)-point for (R o S)(x).  |
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outermeasure
Member of the 'S.O.S. Math' Hall of Fame
Joined: 29 Dec 2008
Posts: 2054
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
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| Posted: Mon, 9 Nov 2009 15:44:27 UTC Post subject: |
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| Nona M. wrote: | | To find the set of points for (R o S)(x) = R(S(x)), pick an x-value from S, find the corresponding y-value for S, plug this into R as an x-value, and find the corresponding y-value for R. The x-value for S and the y-value for R are an (x,y)-point for (R o S)(x). |
I think Susan123456 meant composing relations, not functions (since obviously S is not a function in the strict sense with (3,4) and (3,1) both in S).
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Susan123456
Senior Member
Joined: 18 Jul 2008
Posts: 114
Location: California, USA
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| Posted: Tue, 10 Nov 2009 03:34:54 UTC Post subject: |
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I actually solved my own problems. I just have to use the definition of relational composition. Thanks guys for your help.
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