Let a = {X ∈ Z : 0 ≤ X ≤ 12}. Show That R = {(A, B) : A, B ∈ A, |A – B| is Divisible by 4}Is an Equivalence Relation. Find the Set of All Elements Related to 1. Also Write the Equivalence Class [2] - Mathematics | Shaalaa.com

A relation R defined on set A=\{x: x \in Z and 0 \leq x \leq 10... | Filo

Q19. Let A=\{1,2,3, \ldots, 100\}. Let a relation R be defined ... | Filo

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An equivalence relation R in A divides it into equivalence classes A1

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