Can you relate which school buses go to which schools? Not any bus can go to any school! So, does there exist a relation between them? The buses with a school name written on it will belong to that particular school. Therefore, the school name as a function defines the relation between buses and schools. Interesting? Let’s read all about a relation and function in the topics below.
- Types of Relations
- Types of Functions
- Representation of Functions
- Composition of Functions and Invertible Function
- Algebra of Real Functions
- Cartesian Product of Sets
- Binary Operations
FAQ on Relations and Functions
Question 1: What is the difference between relation and function?
Answer: A relation refers to a set of inputs and outputs that are related to each other in some way. In other words, when each input in relation gets precisely one output, we refer to the relation as function. Moreover, in order to determine whether a relation is a function or not, you need to make sure that no input gets more than one output.
Question 2: What are the types of relations?
Answer: In math, there are nine kinds of relations which are empty relation, full relation, reflexive relation, irreflexive relation, symmetric relation. Further, there is antisymmetric relation, transitive relation, equivalence relation, and finally asymmetric relation.
Question 3: What does the Cartesian Product of Sets mean?
Answer: The Cartesian product of sets refers to the product of two non-empty sets in an ordered way. Thus, basically, it is the collection of all ordered pairs which we attain by the product of two non-empty sets. In other words, an ordered pair means that two elements are derived from each set.
Question 4: What is an invertible function?
Answer: An invertible function is if on reversing the order of mapping you get the input as the new output. That is to say, if a function, of whose domain is in set Y and image in set Z is invertible if f-1 has its domain in Z and image in Y.