The most difficult part to understand was the idea of a relation being transitive. I did not understand it until I was given examples of specific relations and what it mean for them to be transitive or not. Being transitive is to say that if a relates to b and b relates to c then a relates to c. An example of a transitive relation is the divides. Like if a divides b and b divides c then a divides c for real numbers a, b, c.
Knowing the properties of certain relations can be quite helpful as one tries to manipulate a given result to prove or disprove it. One can know useful ideas that we used in induction such as if a > b and b > c then a > c. But it would be a mistake to say if a is not equal to b and b is not equal to a then a is not equal to a. Keeping in mind the properties allows for steps to be taken that could not otherwise be taken.
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