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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 = {(1,2), (2,3), (2,4), (3,1), (3,2), (4,1), (4,4)} (ii) R = {(a,b): a2 + b2 > 10} (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 + 2b is divi ...

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