How can I test the properties of the following relation:
R={((a,b),(c,d)): ad=bd } where a,b,c and d real numbers.
We used to test the properties for only two variables!!
Please anyone have any idea???
Thank you.
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1Could you specify which "properties" you mean? Are you sure that it is $ad=bd$ and not $ad=bc$? – Patrick May 10 '14 at 12:04
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Reflexive, symmetric and transitive. This is a question our prof. gave us. – May 10 '14 at 12:06
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if it is $ad=bc$, see http://math.stackexchange.com/questions/785554/equivalence-relation-and-classes-confusion/785565#785565 – Eleven-Eleven May 10 '14 at 12:16
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@Eleven-Eleven Thank you very much. – May 10 '14 at 12:30
2 Answers
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This is a relation on pairs. Where you are accustomed to check e.g. $x \mathrel{R} y$, you'll have to check pairs, like $(u, v) \mathrel{R} (x, y)$
vonbrand
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This relation can be expressed:
Two pairs of real numbers $\vec u$ and $\vec v$ are related iff the two components of $\vec u$ are the same or the second component of $\vec v$ is 0.
If with 'properties' you mean reflexivity, symmetry and transivity, we have:
- It isn't reflexive, since $(2,1)$ isn't related to itself.
- It isn't symmetric, since $(2,1)R(2,0)$ but $(2,0)$ is not related to $(2,1)$
- It isn't transitive: $(2,1)R(0,0)R(1,2)$ but $(2,1)$ isn't related to $(1,2)$.
ajotatxe
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This is the first time I ask for help from a website, and within half an hour I found response.you guys are awesome !! Thank you – May 10 '14 at 12:34