Class 12 Maths - BIHAR
Relations and Functions
The Relations and Functions chapter in Class 12 Mathematics builds upon the basic concepts of sets learned in Class 11. It explores advanced types of relations such as reflexive, symmetric, transitive, and equivalence relations, which are crucial for defining mathematical structures. Students also learn about functions, specifically one-one (injective), onto (surjective), and bijective functions, alongside the concept of invertibility. This chapter is a foundational pillar for calculus and algebra in the Bihar Board (BSEB) curriculum. Mastering it ensures a strong conceptual base, helping students easily score high marks in both objective and subjective questions.
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 all a in A.
Symmetric Relation
A relation R 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 is transitive if (a, b) and (b, c) belonging to R implies that (a, c) also belongs to R.
Equivalence Relation
A relation is called an equivalence relation if it is simultaneously reflexive, symmetric, and transitive.
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 codomain B has at least one pre-image in the domain A.
Important Formulas
Board Exam Info
In the Bihar Board (BSEB) Class 12 Mathematics exam, this chapter typically carries around 6 to 10 marks. Questions usually include 2-3 objective (multiple-choice) questions, one short-answer question (worth 2 marks) testing equivalence relations or function types, and occasionally a long-answer question (worth 5 marks) on proving a function is bijective and finding its inverse.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must separately prove three properties: reflexivity (aRa), symmetry (if aRb then bRa), and transitivity (if aRb and bRc then aRc) for all elements in the set.
What is the easiest way to check if a function is one-one?
Take two arbitrary elements x1 and x2 in the domain, set f(x1) = f(x2), and algebraically solve to show that it strictly results in x1 = x2.
Is it mandatory to find the inverse of a function in board exams if asked?
Yes, if the question asks to show invertibility and find the inverse, you must first prove the function is bijective, and then solve y = f(x) for x in terms of y to write f^(-1)(y).
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