Data Structures, Algorithms, & Applications in C++
Chapter 3, Exercise 17

(a)

Not true. For example, if f(n) = n² and g(n) = 1, then f(n) = O(n²) and g(n) = O(n²). But, f(n)/g(n) = n² != O(1).

(b)

Not true. For example, if f(n) = n² and g(n) = n², then f(n) = O(n⁴) and g(n) = O(n²). But, f(n)/g(n) = 1 != Omega(n²).

(c)

Not true. Follows from (a) and/or (b).

(d)

Not true. For example, if f(n) = n² and g(n) = n², then f(n) = Omega(n²) and g(n) = Omega(1). But, f(n)/g(n) = 1 != Omega(n²).

(e)

Not true. For example, if f(n) = n² and g(n) = 1, then f(n) = Omega(1) and g(n) = Omega(1). But, f(n)/g(n) = n² != O(1).

(f)

Not true. Follows from (d) and/or (e).