Question

Which of the following is an empty set:

A. Ω(g(n)) ∩σ(g(n))
B. Ω(g(n)) ∩ω(g(n))
C. 0(g(n)) ∩σ(g(n))
D. Ω(g(n)) ∩0(g(n))
A) D
B) A
C) B
D) C

Answer 1

The empty set is one where the intersection of two sets results in no common elements. Option B, Ω(g(n)) ∩ ω(g(n)), represents the intersection of a set in big Omega notation and a set in small omega notation, resulting in an empty set.

Step-by-step explanation:

The empty set, also known as the null set, is a set that does not contain any elements. In the given options, an empty set is one where the intersection of two sets results in no common elements.

Option B, Ω(g(n)) ∩ ω(g(n)), represents the intersection of a set in big Omega notation and a set in small omega notation. Since these two notations represent different growth rates, there will be no common elements, resulting in an empty set.

Therefore, the correct answer is Option B.