RELATIONS AND FUNCTION
1 RELATION: Understanding the definition of a relation,types of relations(like one-to-one,many-to-one),and properties of relation.
2fUNCTION: Definition and concept related to functions,including domain,range,and types of functions(such as one-to-one,onto,and bijective).
3COMPOSITION OF FUNCTIONS:The peocess of combining twofunctions to nform a new functiion.
4INVERSE OF A FUNCTION:The concept of finding the inverse function and its properties.
5BINARY OPERATIONS:Understanding operations like addition,substraction,multiplication,and division in the context of sets
Here's a question you might find on relations and functions in this chapter :
OUESTION:
Consider the sets A=1,2,3and B=4,5,6.Define the relation R from AtoB as follows:R=(1,4),(2,5),(3,6).
1. Write down the relation R explicitly.
2. Is the relation r a function?justify your answer .
3. Determine the domain and range of the relation R.
SOLUTION:
1.RELATION R EXPLICITLY:The relation R is given by the set of orderd pairs:
[R={()1,4),(2,5),(3,6)}]
2. Is R a Function?To be a function,each element in the domaian A should be assosiated with exactly one element in the Codomain B.In this case
. 1 is associated with 4
.2 is associated with 5
.3 is associated with 6
Since each element in A is paired with exactlyone element in B,R is indeede a function.
