“Sets, relations, and functions” is one of the most important topics in set theory in mathematics. Sets, relations, and functions are three different words with different mathematical meanings but are all equally important for JEE mains preparation. Let’s take a closer look at the topic in this article to gain a better understanding.

How to study Set, relations, and functions

Sets, Relations, and Functions is a foundational topic or building block for differential and integral calculus, as well as many other chapters, so you must complete it.

  • To grasp this subject, you must first study sets, then relations and finally functions in that order. It will then be simple to understand.
  • Begin by learning basic concepts such as simple definitions (what is a set, what is a relation, and what is a function) under each topic before moving on to the next by going over each concept.
  • Move on to more complex concepts like properties of union and intersection, De-Laws, Morgan’s number of relation and function, and so on once you’ve mastered the basics. Finally, you must be able to connect all of the topics in order to answer the question.
  • After you’ve gone over these concepts, go over some solved examples before moving on to the MCQ and practising the problem to ensure you’ve grasped the material.
  • Solve the questions in the books you’re reading, then look over previous year’s papers.
  • While going over the concepts, make sure you understand the derivation of formulas and try to derive them on your own, as you will often not need the exact formula but some steps of derivation will be very helpful in solving the problem if you understand the derivation.
  •  Since Sets, Relations, and Functions can be geometrically visualized, use Venn diagrams and graphs to understand and relate the concepts. Visualizing a problem makes it easier to comprehend and solve.

There are also pdf available for questions and answers on set, relations, and functions

MCQ on sets relations and functions

Ques1. In certain classes, 15 students play volleyball, 13 play      Cricket, 5 play both games. How many students are there in the class who play only volleyball, only Cricket and the number of the students in the class?

  1. 10
  2. 26
  3. 23
  4. 16

Answer- C

Ques 2- According to a survey, 63 per cent of residents in a city read the newspaper. 76 percent read newspaper A, while 76 percent read newspaper B. If x percent of the population reads both newspapers, then x can have any value.

  1. 55
  2. 29
  3. 65
  4. 37

Answer- B

Ques 4. {0} is equal to:

  1. a) 0
  2. b) Φ      
  3. c) both a) and b)    
  4. d) none.

Answer. D

Conclusion

Sets are collections of well-defined objects; relations indicate relationships between members of two sets A and B; and functions are a special type of relationship where there is exactly (or at most) one relationship for each element ∈A with an element in B. A set is a collection of distinct objects that do not contain any duplicates.

R (A, B) is a binary relation in which the set A and B is a subset of A and B’s Cartesian product (A B). The notation aRb denotes that a and b have a relationship and that (a, b) R. A total function f: A B is a special relationship in which there is exactly one element b B for each element A. The formula is f(a) = b. The difference between a partial and a total function is that a partial function may be undefined for one or more values of A.