## 1.1 Relations: Introduction

What are relations?

In every day life, a person is related to their parents, siblings, cousins, teachers, friends, etc. in some way. Similarly in mathematics, mathematical objects like numbers and sets are related to one another in some way. Many relations (symbols) will be familiar already:

Consider the following set We can compare the numbers in A using the symbol “<” as follows: etc. We can write this as a set in the following way:

Each pair in this new set R expresses the relationship x < y (where x and y are numbers from A).

In other words, So if asked whether is true, one only needs to look into our set R to find the pair If we didn’t find it, then the relation would be considered false for the given set. The above example is intuitive because we are already comfortable with the relation <. In more abstract cases, thinking of the relationship between mathematical objects in this way may be a little trickier!…