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Show that the relation S in set A = {x ∈ Z : 0 ≤ x ≤ 12} given by S = {(a, b); a, b ∈ A, |a - b| is divisible by 4} is an equivalence relation.

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Show that the relation S in set A = {x ∈ Z : 0 ≤ x ≤ 12} given by S = {(a, b); a, b ∈ A, |a - b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.

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Given relation is S = {(a, b) : |a - b| is divisible by 4 and a,b ∈ A}.

 

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