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Math Help - Miscellaneous Discrete Math help, please.

  1. #1
    Mad
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    Exclamation Miscellaneous Discrete Math help, please.

    I'm really sorry about posting all of these problems but I wasn't sure if I should post them individually or not. I'm trying to help my boyfriend because I've had Discrete Math but he's covering stuff I didn't and I learned stuff he's not so it's not really working out and I hate to let him down what with how busy he is. If someone could help me understand them I could then help him when he gets back from babysitting his brother at school...don't ask.


    Any help with any problem would be greatly appreciated.



    Problem 24: Show that at least 3 of any 25 days chosen must fall in the same month of the year


    I have no idea about this one... O_O


    Problem 4: Use a proof by cases to show that min(a, min(b,c))=min(min(a,b),c) whenever a, b and c are real numbers.


    This one reminds me of working with arrays but I'm not sure if I'm thinking of it correctly. But here is my guess:


    min(a, min(b,c)) = min(min(a,b), c)
    min(a, b) = min(a, c)
    a = a


    Problem 18: Prove that given a real number x there exist unique numbers n and e such that x = n - e, n is an integer and 0 <= e < 1.


    Don't understand...


    Problem 28: Prove that there are no solutions in integers x and y to equation 2x^2+5y^2=14


    Don't understand this either...

    Problem 2: Use set builder notation to give a description of each of these sets:
    a. {0,3,6,9,12}
    b. {-3,-2,-1,0,1,2,3}
    c. {m,n,o,p}

    I know what set builder notation is but what does it mean to give a description of a set?


    Problem 14: Use a Venn diagram to illustrate the relationship A proper subset of B and B proper subset C.


    I know how to do Venn Diagrams but I don't know what A proper and B proper and whatever is.


    Problem 16: Find two sets A and B such that A member of B and A perfect subset of B


    Not sure about this one either.
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  2. #2
    Member
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    k

    Quote Originally Posted by Mad View Post
    Problem 24: Show that at least 3 of any 25 days chosen must fall in the same month of the year
    If 25 days are chosen, then the first 24 may be selected by taking 2 days from each of the 12 months. At this point, the 25th day must be selected from one of the 12 months causing that month to have at least 3 days selected.


    Quote Originally Posted by Mad View Post
    Problem 4: Use a proof by cases to show that min(a, min(b,c))=min(min(a,b),c) whenever a, b and c are real numbers.


    This one reminds me of working with arrays but I'm not sure if I'm thinking of it correctly. But here is my guess:


    min(a, min(b,c)) = min(min(a,b), c)
    min(a, b) = min(a, c)
    a = a
    With cases means that you need to consider the following cases:
    a<=b<=c, a<=c<=b, c<=a<=b, c<=b<=a, b<=a<=c, b<=c<=a

    It appears your attempt is one of those cases, now just supply the rest.




    Quote Originally Posted by Mad View Post
    Problem 2: Use set builder notation to give a description of each of these sets:
    a. {0,3,6,9,12}
    b. {-3,-2,-1,0,1,2,3}
    c. {m,n,o,p}

    I know what set builder notation is but what does it mean to give a description of a set?
    You need to come up with rules that will build the given set.

    a. {x|x=3n, n is an element of the integers and -1<n<5}


    Have fun
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