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.

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Expert Answer

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:

Algebra homework question answer, step 2, image 1
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Step 3

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

Algebra homework question answer, step 3, image 1
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