Math Is Fun Forum

I'm working out of a friend's textbook to try and prepare myself for a class I'll be taking in a month or so. I was wondering if someone could give me the answers to these problems so I have a better understanding of how to solve them?

1) How do you figure the degree of the table?

Let A_i, 1 ≤ i ≤ 5, be the domains for a table D ⊆ A_1 x A_2 x A_3 x A_4 x A_5, where A_1 = {U, V, W, X, Y, Z} (used as code names for different cereals in a test), and A_2 = A_3= A_4 = A_5 = Z^+.

Table D:

Code Name of Cereal / Grams of Sugar per 1-oz Serving / % of RDA^a of Vitamin A per 1-oz Serving / % of RDA Vitamin C per 1-oz Serving / % of RDA of Protein per 1-oz Serving
U    1    25    25    6
V    7    25    2    4
W    12    25    2    4
X    0    60    40    20
Y    3    25    40    10
Z    2    25    40    10

2) How do you determine the best "big-Oh" form?

Use the results of Table 1 to determine the best “big-Oh” form for the following function f: Z^+→ R.
f(n) = 3n + 7

Table 1 (I'm not sure how to write tables so I used the dash (-----):

Big-Oh Form ------------------------ Name
O(1) --------------------------------- Constant
O(log_2 n) -------------------------- Logarithmic
O(n) --------------------------------- Linear
O(n log_2 n) ------------------------ n log_2 n
O(n^2) ------------------------------ Quadratic
O(n^3) ------------------------------ Cubic
O(n^m), m = 0, 1, 2, 3,... ------- Polynomial
O(c^n), c > 1 ----------------------- Exponential

I'm practicing some discrete math from a friend's textbook.  My class isn't for a month, but I am struggling so far (I knew I would as I haven't taken a math course in several years).  I'm working on exercises in the book and found these 2 problems to be quite confusing.

1) If a, b, c ∈ Z^+ and a|bc, does it follow that a|b or a|c?

2) For each of the following pairs, a, b ∈ Z^+,  determine gcd(a, b) and express it as a linear combination of a, b.

231, 1820

Any help on how to solve these is greatly appreciated.

A bit confused on how to begin this.

Consider the permutation of 1, 2, 3, 4. The permutation 1432, for instance, is said to have one ascent – namely, 14 (since 1 < 4). This same permutation also has two descents – namely, 43 (since 4 > 3) and 32 (since 3 > 2). The permutation 1423, on the other hand, has two ascents, at 14 and 23 – and the one descent 42.

a) How many permutations of 1, 2, 3 have k ascents, for k = 0, 1, 2?