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Math Help - Inclusion-Exclusion theorm

  1. #1
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    Inclusion-Exclusion theorm

    Any help would be appreciated...I'm rather stuck!
    It's a mock exam and annoyingly they provided no solutions for me to work from...grrr....

    Thank-you
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Inclusion

    Solution for 1a in line 2.

    For 1b think a little!
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Inclusion

    Solution for 1a in line 2.

    For 1b think a little!
    I'll type out what i've written =)...the main problem i'm having is i don't know if it is right! Or even how i'm doing it is right...
    ty for reply
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    Using the floor function there \left\lfloor {\frac{{50}}<br />
{3}} \right\rfloor  = 16 of those 50 numbers divisible by 3.
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    Quote Originally Posted by Plato View Post
    Using the floor function there \left\lfloor {\frac{{50}}<br />
{3}} \right\rfloor  = 16 of those 50 numbers divisible by 3.
    But then how would it be possible to work out without writing out all the numbers(for example A n B)? I was under the impression the question should be calculated without doing that?

    Thanks
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  6. #6
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    Quote Originally Posted by AshleyT View Post
    But then how would it be possible to work out without writing out all the numbers(for example A n B)? I was under the impression the question should be calculated without doing that?
    It is not possible to do that easily.
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    Quote Originally Posted by Plato View Post
    It is not possible to do that easily.
    So i would have to go through and write all the numbers out basically?
    I don't see the point of that using the inclusion-exclusion theorm...arg...this is the annoying thing about not having the solutions...don't know how they want us to do it...

    Thankyou for your reply Plato

    EDIT: WAIT NEVER MIND I GET IT NOW!! Silly me was thinking it was the actual numbers, rather than how many were in the set!

    Thankyou!!
    Last edited by AshleyT; December 8th 2010 at 10:01 AM.
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  8. #8
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    Quote Originally Posted by AshleyT View Post
    So i would have to go through and write all the numbers out basically?
    I don't see the point of that using the inclusion-exclusion theorm...arg...this is the annoying thing about not having the solutions...don't know how they want us to do it.
    The answer is clear:
    \left\lfloor {\frac{{50}}<br />
{2}} \right\rfloor  + \left\lfloor {\frac{{50}}<br />
{3}} \right\rfloor  + \left\lfloor {\frac{{50}}<br />
{5}} \right\rfloor  - \left\lfloor {\frac{{50}}<br />
{6}} \right\rfloor  - \left\lfloor {\frac{{50}}<br />
{{10}}} \right\rfloor  - \left\lfloor {\frac{{50}}<br />
{{15}}} \right\rfloor  + \left\lfloor {\frac{{50}}<br />
{{30}}} \right\rfloor
    That is using the inclusion-exclusion.
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  9. #9
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    Hey, sorry i just edited my post before i saw your reply! I was misreading the formula... and i was working with a friend who said we should be writing out the numbers lol...

    Thankyou for your help plato =)
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