代写MATH 3175 GROUP THEORY QUIZ 2代写留学生Matlab程序

QUIZ 2 (20 MIN, OPEN BOOK)

MATH 3175 GROUP THEORY

(Each problem is worth 10 points.)

(1) (a) Give the addition and multiplication table of Z6 = {0, 1, 2, 3, 4, 5} where a = [a]6.

(b) What are the units and zero divisors in Z18?

(2) Suppose that n > 1 is an integer and [a]n, [b]n ∈ Zn such that [a]n[b]n is a zero divisor.

Prove that [a]n or [b]n is a zero divisor.

(3) For each function below answer the following questions:

• Is the function onto?

• Is the function one-to-one?

(a) f : [0, ∞) → [0, ∞) defined by f(x) = x 2 .

(b) g : Z → Z defined by g(x) = x 3 .

(c) h : R → R defined by h(x) = sin(x).