anonymous
  • anonymous
Let X = {5, 10, 15, 20, 25, 30, 35, 40}. Define a relation on X as follows. For a, b is in X, a b if b can be obtained from a by adding a (possibly empty) collection of dimes (10 cents) and quarters (25 cents). So, for example, 25 35, but 25 30. List all minimal elements of (X, ). (Enter your answers as a comma-separated list
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
http://www.awesomescreenshot.com/image/454102/5c442f15a749a336294b889e959b94fb
anonymous
  • anonymous
lets start with 5 you cannot add 10 or 25 to 5 to get 10 but you can add 10 to 5 to get 15, so \(5R15\)
anonymous
  • anonymous
check my screen shoot,and let me know correct answer only

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anonymous
  • anonymous
refresh my memory what does "minimum elements" of a relation mean?
anonymous
  • anonymous
I don't know i am stuck with this queston, I don't know
anonymous
  • anonymous
so can u help mam
pooja195
  • pooja195
reference for the definition of a minimal set: http://ndp.jct.ac.il/tutorials/discrete/node34.html
pooja195
  • pooja195
I think minimal element is such that it cannot be the result of the relation . So out of {5,10,15,20....}, we cannot get 5 or 10 by the operation.
anonymous
  • anonymous
this is obvious and already written in my question,i have not asked this... i think u must read my question again, don't repeat question sentences in answer again
pooja195
  • pooja195
No i think you should read the reply again.
mathmath333
  • mathmath333
she is saying the answer is \(\{15,20,25,30,35,40\}\)
mathmath333
  • mathmath333
i think
pooja195
  • pooja195
I was doing the 2nd one first since it was easier :/ sorry about that! The second one should be 5 and 10 no operation goes into those numbers
pooja195
  • pooja195
@meneedy Do u understand?
anonymous
  • anonymous
{15,20,25,30,35,40} is is my answer
pooja195
  • pooja195
No .-.
anonymous
  • anonymous
then?
pooja195
  • pooja195
\(\color{#0cbb34}{\text{Originally Posted by}}\) @pooja195 I think minimal element is such that it cannot be the result of the relation . So out of {5,10,15,20....}, we cannot get 5 or 10 by the operation. \(\color{#0cbb34}{\text{End of Quote}}\) Therefore 5 and 10 would be the answers
anonymous
  • anonymous
ohh,
pooja195
  • pooja195
5,10
pooja195
  • pooja195
Rember that minimal elements cannot be obtained as a result of the relation.
anonymous
  • anonymous
yes, i understand it,
anonymous
  • anonymous
cool
pooja195
  • pooja195
Good :)
pooja195
  • pooja195
\(~~~~~~~~~~~~~~~~~~~~~~~~~~\Huge{\color{red}{\heartsuit}\color{orange}{\bigstar}\color{yellow}{\heartsuit}\color{green}{\bigstar}\color{blue}{\heartsuit}\color{purple}{\bigstar}\color{hotpink}{\heartsuit}}\)\(\Huge\bf\color{#FF0000}W\color{#FF4900}e\color{#FF9200}l\color{#FFDB00}c\color{#FFff00}o\color{#B6ff00}m\color{#6Dff00}e\color{#24ff00}~\color{#00ff00}t\color{#00ff49}o\color{#00ff92}~\color{#00ffDB}O\color{#00ffff}p\color{#00DBff}e\color{#0092ff}n\color{#0049ff}S\color{#0000ff}t\color{#2400ff}u\color{#6D00ff}d\color{#B600ff}y\color{#FF00ff}!\)\(~~~~~~~~~~~~~~~~~~~~~~~~~~\Huge{\color{red}{\heartsuit}\color{orange}{\bigstar}\color{yellow}{\heartsuit}\color{green}{\bigstar}\color{blue}{\heartsuit}\color{purple}{\bigstar}\color{hotpink}{\heartsuit}}\)\(\Large\bf\color{Lime}{Please,\ don't\ hesitate\ to\ ask\ questions!}\)\(\Large\bf\color{magenta}{We're\ here\ to\ help!}\Large\color{magenta}{\ddot\smile}\)
anonymous
  • anonymous
Can you help me 2 more questions?
pooja195
  • pooja195
You'll need to re-post them again
anonymous
  • anonymous
okay

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