Question

Asked Jan 26, 2020

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Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by

(i) R = {(a, b) : |a – b| is a multiple of 4}

(ii) R = {(a, b) : a = b}

is an equivalence relation. Find the set of all elements related to 1 in each case.

Step 1

Given: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by

(i) R = {(a, b) : |a – b| is a multiple of 4}

(ii) R = {(a, b) : a = b}

is an equivalence relation. Find the set of all elements related to 1 in each case.

Step 2

Concept used:

Step 3

Here, A = {x ∈ Z : 0 ≤ x ≤ 12} = {1,2,3,4,5,6,7,8,9,,10,11...

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