Question

Which of the following statements is a correct interpretation of the proof regarding the Big O notation being closed under addition?

a) f⋅h is always equal to O(g).
b) f⋅h is never equal to O(g).
c) If f and h are both O(g), then f⋅h is also O(g).
d) The proof does not provide enough information about f⋅h.

Answer 1

The correct interpretation of the proof regarding the Big O notation being closed under addition is that if both functions f and h have an upper bound represented by the function g, then the product of f and h also has an upper bound represented by g.

Step-by-step explanation:

The correct interpretation of the proof regarding the Big O notation being closed under addition is option c) If f and h are both O(g), then f⋅h is also O(g).

This means that if both functions f and h have an upper bound represented by the function g, then the product of f and h also has an upper bound represented by g.

For example, if f(n) = 2n and h(n) = 3n, and the upper bound for both functions is g(n) = 5n, then the product f(n)⋅h(n) = 2n⋅3n = 6n^2 also has an upper bound represented by g(n) = 5n.