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.
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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