Question: Intro to discrete math We define ~ as on the SCC graph: 8= {(v, v') E V/ | In EN, 3vo, . .., Un

Intro to discrete math

We define ~ as " on the SCC graph": 8= {(v, v') E V/ | In EN, 3vo, . .., Un EV/s, V0 = VAUn = VAVie {1, ..., n}, (vi-1, vi) ET/}. Exercise 6. Answer the following questions, each time proving your claim: 1. Is reflexive? 2. Is ~ symmetric? 3. Is ~antisymmetric? Hint: Prove the following lemma: Lemma. For any vertices [vo, [U']s E V/s, if [ulo ~ ['l then v v. 4. Is ~ transitive? 5. Is an equivalence relation? 6. Is an order relation? If yes, is it total? Note: In this exercise we consider ~ not over a particular graph, but in general. So when the answer is yes, a proof must be for any graph, but when the answer is no, a counterexample can be from a particular graph (from Go/ for instance).\f

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