# MTH202 ASSIGNMENT 1 SOLUTION 2021 LEARNINGSTECH.COM

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Solution (i) if r is reflexive, then r-1 is reflexive.. Assume that the relation r on a is reflexive. By using definition, ∀ a ∈ a, (a, a) ∈r. In view that r-1 consists of precisely those ordered pairs which can be obtained with the aid of  interchanging the first and second detail of ordered pairs in r, consequently, if (a, a) ∈ r then (a, a) ∈ r-1. Thus, ∀ a ∈ a, (a, a) ∈ r-1. As a result r-1is reflexive as properly. Answer (ii) assume that the relation r on a is symmetric. Let (a, b) ∈ r-1for a,b ∈a. By means of definition of r-1, (b, a) ∈r. Since r is symmetric.