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Math Help - equivalence classes

  1. #1
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    Exclamation equivalence classes

    The Question: A marketing agency conducted a survey of 5000 people. The same list of 5 current television programs was presented to each person, who was then asked to state which of those programs he or she regularly watched. In analyzing the results, the agency defined an equivalence relation R on the set of 5000 people as follows: for any people x and y,
    xRy <-> x regularly watches exactly the smae programs in the list as y does.
    How many different equivalence classes can there be for this equivalence relation? Why?

    now my question: how do you go about determining the number of equivalence classes (for any problem).
    Thank-you in advance
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  2. #2
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    Reflexsive A person watches as much television as himself.

    Symettric If a person watches as much television as another person then the other person watches as much television as the first person.

    Transitive If a person watches as much television as a second person and that second person watches as much as a third person then the first person has to watch as much television as the third person.

    Now you create equivalence classes. You can have as many equivalence classes as you want. You can have all people watching 1 hour so you have 1 equivalence class of 5000 people. Or you can have equivalence classes of 1 each. Every person watches a different program (unless are told to use pigeonhole principle if there is a limit).
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    Reflexsive A person watches as much television as himself.

    Symettric If a person watches as much television as another person then the other person watches as much television as the first person.

    Transitive If a person watches as much television as a second person and that second person watches as much as a third person then the first person has to watch as much television as the third person.

    Now you create equivalence classes. You can have as many equivalence classes as you want. You can have all people watching 1 hour so you have 1 equivalence class of 5000 people. Or you can have equivalence classes of 1 each. Every person watches a different program (unless are told to use pigeonhole principle if there is a limit).
    I think it's not question of how much people watch certain programs but what programs they watch independent of amount of time they spent on watching them.

    It's a matter of list of programs they watch, so it would be:
    Reflexive xRx because same person watch same list of programs.
    Symettric xRy and yRx because two persons watch same list of programs.
    Transitive xRy and yRz -> xRz because all persons watch same list of programs.

    Now this becomes question of combinations of list of programs that people are regularly watch.
    So, if we have choice of 5 programs we must calculate how many different combinations of those programs can be:
    5/1=5
    5*4/1*2=10
    5*4*3/1*2*3=10
    5*4*3*2/1*2*3*4=5
    5*4*3*2*1/1*2*3*4*5=1

    So there can be 5+10+10+5+1 = 31 different list of programs that people can watch regularly.

    So there can be 31 equivalence classes of people who are watching same list of programs.
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