Question

Match each of the following asymptotic notation with their correct definition. f(n) and g(n) are some functions ; a and b are constants.

1. Big-θ notation
2. Big-O notation
3. Big-Ω notation
1) Big-θ notation represents the upper bound of a function.
2) Big-O notation represents the lower bound of a function.
3) Big-Ω notation represents the tight bound of a function.
4) Big-θ notation represents the lower bound of a function.
5) Big-O notation represents the tight bound of a function.
6) Big-Ω notation represents the upper bound of a function.

Answer 1

Big-θ notation represents the upper bound, Big-O notation represents the upper bound, and Big-Ω notation represents the lower bound of a function.

Step-by-step explanation:

The correct matches between the asymptotic notations and their definitions are:

1. Big-θ notation represents the upper bound of a function.
2. Big-O notation represents the upper bound of a function.
3. Big-Ω notation represents the lower bound of a function.

Remember that Big-θ notation represents both the upper and lower bounds of a function, while Big-O and Big-Ω notation only represent the upper and lower bounds respectively. It's important to understand the definitions and applications of these notations when analyzing the time complexity of algorithms.