1. For each of the following relations R on the set A = {1,2,3,4}

| February 14, 2018

1. For each of the following relations R on the set A = {1,2,3,4}, find the matrix
representing R and draw the directed graph corresponding to R.
(i) R = {(1,3), (2,3), (2,4), (3,1), (3,2), (4,2), (4,4)}
(ii) R = {(a,b): a2 + b2 > 8}
(iii) R = {(a,b): a – b > 0}
2. Given the following relations R on the set of non-negative integers, test whether R
satisfies each of the properties of an equivalence relation.
(i) R = {(a,b): a –b is divisible by 4}
(ii) R = {(a,b): a + 3b is divisible by 4}

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