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Define partitions on the set of integers

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Indicate whether each of the following define partitions on the set of integers. Explain your answer.

A: The sets of odd and even integers

b The sets of positive and negative integers

c: The set of integers greater than 100 and the set of integers less than 200

D:The set of all integers

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question   

Consider the set S defined in problem 4 (detail above) and the following relation = defined on S as follows: (x1, y1) = (x2, y2) if x1 + y1 = x2 + y2.

Draw the directed graph of this relation. Show that it is an equivalence relation. List its equivalence classes.

Reference no: EM131251582

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