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Math Help - Set Theory

  1. #1
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    Set Theory

    Any explanation with regards to solutions would be GREATLY appreciated.
    Attached Thumbnails Attached Thumbnails Set Theory-image.jpg  
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  2. #2
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    Re: Set Theory

    I think I have managed to determine that the answer to number 1 is C...
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  3. #3
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    Re: Set Theory

    I also think I understand number 2... If someone could explain how to calculate the total time, and explain a critical path?
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  4. #4
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    Re: Set Theory

    Note we have a 3-way branch at A, and 2-way branchings at C and D, all other nodes have no choice of path.

    So our possible paths start:

    AB
    AC
    AD

    the first path has only one completion:

    ABEH

    the next path can go one of two ways:

    ACE...
    ACF...

    after that, we can only complete each of THOSE one way:

    ACEH
    ACFH

    finally, we can go one of two ways after AD:

    ADF...
    ADG...

    and these both can be completed only one way:

    ADFH
    ADGH, giving 5 paths in all:

    ABEH
    ACEH
    ACFH
    ADFH
    ADGH

    To compute the time required for completing the task, we add the times required for each individual task:

    Time for ABEH, for example, is 3+7+8+5 = 23 days.

    Calculate the times for the other 4 complete task paths, the critical path is the one with the shortest completion time.

    To find the critical path for F, treat F as if it were the "end-stage" of the assembly product.
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