Question: 2. (10 marks) Let the relation on Z be defined by xuy if and only if x = y (mod 4). (i) (1 mark)

2. (10 marks) Let the relation on Z be defined by xuy

2. (10 marks) Let the relation on Z be defined by xuy if and only if x = y (mod 4). (i) (1 mark) Is reflexive? (ii) (2 marks) Isu symmetric? (iii) (2 marks) Is antisymmetric? (iv) (2 marks) Is transitive? (v) (2 marks) Is is an equivalence relation? If so determine the equivalence classes. (vi) (1 marks) Is a partial order? In all cases justify your answer.

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i To determine if the relation on Z is reflexive we need to check if for every element x in Z xx holds true In this case x x mod 4 is always true because the two sides of the congruence are equal Ther... View full answer

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