4.7 - Lower Bounds and Θ Notation

Big-Theta notation (Θ) defines an equivalence relation on the set of functions.

True

Determine the proper relationship between the following pair of functions. f(n) = 2^​n​​, g(n) = 3^n

f(n)is O(g(n))

Determine the proper relationship between the following pair of functions. f(n) = 2^​n​​, g(n) = n^n

f(n)is O(g(n))

Determine the proper relationship between the following pair of functions. f(n) = √​n, g(n) = log (n^2)

f(n)is Ω(g(n))

The Sequential Search algorithm is Θ(n^2).

False

The Sequential Search algorithm is Θ(n^n).

False

Determine the proper relationship between the following pair of functions. f(n) = 2^​n​​, g(n) = 10n​^2

f(n)is Ω(g(n))

Determine the proper relationship between the following pair of functions. f(n) = 2^​n​​, g(n) = n log n

f(n)is Ω(g(n))

Determine the proper relationship between the following pair of functions. f(n) = log^2 n, g(n) = logn

f(n)is Ω(g(n))

Determine the proper relationship between the following pair of functions. f(n) = n. g(n) = log^2 n

f(n)is Ω(g(n))

Determine the proper relationship between the following pair of functions. f(n) = nlogn + n, g(n) = logn

f(n)is Ω(g(n))

For what value of k is √​n ​​​= Θ(n​^k​​)?

0.5