Indicate whether each of the following define partitions on

Question

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

STart question from here

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.