GATE CS 2023 Set 1 — Question 29
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Question
Let and be functions of natural numbers given by and . Which of the following statements is/are TRUE?
Correct answer
(A) f ∈ O(g); (C) f ∈ o(g)
Solution
Given and :
1.Big-O (): if there exist constants and such that for all . This is true for . Thus, (A) is TRUE.
2.Little-o (): if . Here, . Thus, (C) is TRUE.
3.Big-Omega (): if there exist constants and such that for all . This is false because grows strictly faster than . Thus, (B) is FALSE.
4.Big-Theta (): if and . Since is false, (D) is FALSE.
Therefore, statements (A) and (C) are TRUE.Continue learning with Success Tracker
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