Class 12 Maths - RAJASTHAN
Relations and Functions
The 'Relations and Functions' chapter in Class 12 Mathematics for Rajasthan (RBSE) students builds upon the foundational concepts of sets learned in Class 11. It explores advanced classifications of relations such as reflexive, symmetric, transitive, and equivalence relations. Furthermore, students delve deeper into functions, studying one-one (injective), onto (surjective), and bijective functions, along with the concept of invertible functions and binary operations. This chapter is vital for the Rajasthan Board examinations as it forms the basis of calculus and abstract algebra, consistently appearing in both short answer and long answer questions.
Start Learning FreeKey Concepts
Reflexive Relation
A relation R on a set A is reflexive if every element 'a' in A is related to itself, meaning (a, a) belongs to R for all a in A.
Symmetric Relation
A relation R on a set A is symmetric if whenever (a, b) belongs to R, then (b, a) must also belong to R for all a, b in A.
Transitive Relation
A relation R on a set A is transitive if whenever (a, b) and (b, c) belong to R, then (a, c) must also belong to R.
Equivalence Relation
A relation that is simultaneously reflexive, symmetric, and transitive is known as an equivalence relation.
One-One Function (Injective)
A function f: A -> B is one-one if distinct elements of A have distinct images in B, i.e., f(x1) = f(x2) implies x1 = x2.
Onto Function (Surjective)
A function f: A -> B is onto if every element in the co-domain B has at least one pre-image in the domain A.
Important Formulas
Board Exam Info
In the Rajasthan (RBSE) Class 12 Mathematics board examination, this chapter typically carries around 6 to 8 marks. Questions usually include verifying whether a given relation is an equivalence relation, proving a function is bijective, and finding the inverse of a given invertible function.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must mathematically prove that the relation satisfies all three properties: Reflexive, Symmetric, and Transitive, using general elements from the given set.
What is the easiest way to check if a function is one-one and onto?
To check one-one, assume f(x1) = f(x2) and solve to get x1 = x2. To check onto, set y = f(x) and express x in terms of y, ensuring every y in the co-domain yields a valid x in the domain.
Are binary operations important for the RBSE board exam?
Yes, questions on checking commutativity and associativity of binary operations are frequently asked as short or very short answer questions.
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