Class 12 Maths - MAHARASHTRA
Relations and Functions
The 'Relations and Functions' chapter in Class 12 Mathematics under the Maharashtra State Board (MSBSHSE) builds upon the foundational knowledge of sets from Class 11. It explores advanced types of relations such as reflexive, symmetric, transitive, and equivalence relations. Furthermore, it delves deep into functions, focusing particularly on one-one (injective), onto (surjective), and bijective functions, along with the concept of the inverse of a function and binary operations. This chapter is vital for board exams as it forms the theoretical backbone of calculus and algebra, frequently appearing in both MCQ and descriptive sections.
Start Learning FreeKey Concepts
Reflexive Relation
A relation R on a set A is reflexive if every element relates to itself, meaning (a, a) belongs to R for every a in A.
Symmetric Relation
A relation R on a set A is symmetric if whenever (a, b) belongs to R, then (b, a) also belongs to R for all a, b in A.
Transitive Relation
A relation R 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 in the domain have distinct images in the co-domain, 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 Maharashtra (MSBSHSE) Class 12 Mathematics board examination, this chapter typically carries around 4 to 6 marks with options. Questions generally include 1-mark multiple-choice questions, 2-mark short answer questions testing whether a given relation is an equivalence relation, and 3-mark questions on checking the invertibility of functions.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must prove three separate conditions: show it is reflexive, show it is symmetric, and show it is transitive using algebraic steps.
What is the difference between one-one and onto functions?
A one-one function ensures no two domain elements map to the same co-domain element, while an onto function ensures no element in the co-domain is left unmapped.
Is every function invertible?
No, a function is invertible if and only if it is both one-one and onto (bijective).
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