SOLVED: Problem 1: (10 points) Let positive integer n. Partition the following set of 15 functions into equivalence classes such that f(n) and g(n) are in the same equivalence class if and only if f(n) = O(g(n)) (base of logarithm is not specified. It is assumed to be equal to 2.)1. 9log(n)2. 8e^2 2^(2n) log(4^n)3. nlog(n)4. 3^n n^25. log(s^2)(25n)6. t^n!7. log(2)(√n)Then arrange the equivalence classes into sequence C1, C2, C3 such that for any f(n) ∈ C1 and g(n) ∈ C2, f(n) = O(g(n)

SOLVED: Define a relation R on the set of all integers Z: by xRy iff x  y = 2k for some integer k: Verify that R is an equivalence relation and describe the equivalence class E5. How many distinct equivalence classes are there?

Boundary Value Analysis and Equivalence Partitioning