number 9 Let R be the relation from E = {2, 3, 4, 5} to F = {3, 6, 7, 10} which

Question

number 9

Let R be the relation from E = {2, 3, 4, 5} to F = {3, 6, 7, 10} which is defined by the sentence 'x divides y'. Write R as a set of ordered pairs and find its domain and range. Let E = {1, 2, 3, 4, 5}. Verify the relation R = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (3, 4), (4, 3), (4, 4), (5, 5)} is an equivalence relation in E. What is the corresponding partition of E based on such R? Let R be the relation in the set of natural numbers N defined by the sentence (x - y) is divisible by 2', that is, R = {(x, y) | x N, y N, s|(x - y)} Show that R is an equivalence relation.

Explanation / Answer

Given E = {2,3,4,5} and F = {3,6,7,10}

Relation R is defined from E to F such that 'x divides y'. Therefore, for every (x,y) to be an element of R, x must divide y.

Therefore, R = {(2,6), (2,10), (3,3), (3,6), (5,10)}

Hence, domain of relation R is {2,3,5} and range of relation R is {3,6,10}

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