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.