Solving Discrete Mathematics Questions:
1. After a weekend at the Mohegan Sun Casino, Gary finds that he has won $1020-in $20 and $50 chips. If he has more $50 chips than $20 chips, how many chips of each denomination could he possibly have?
2. If there are 2187 functions f : A→B and |B| = 3, what is |A|?
3. Let A ⊆ {1, 2, 3, . . . , 25} where |A| = 9. For any subset of A let sB denote the sum of the elements in B. Prove that there are distinct subsets C, D of A such that |C| = |D| = 5 and sC = sD.
4. Let g: N→N be defined by g(n) = 2n. If A ={1, 2, 3, 4} and f : A→N is given by f _ {(1, 2), (2, 3), (3, 5), (4, 7)}, find g ? f .
5. Let a1, a2, a3, . . . be the integer sequence defined recursively by
a. a1 =0; and
b. For n > 1, an = + a[n/2].
Provide step by step calculations.