Class 12 Maths - HARYANA
Relations and Functions
The 'Relations and Functions' chapter in Class 12 Mathematics builds upon your previous knowledge by introducing advanced classifications of relations such as reflexive, symmetric, transitive, and equivalence relations. It also covers types of functions including one-one (injective), onto (surjective), and bijective functions, alongside the concept of invertible functions and binary operations. This chapter is vital for the Haryana Board (BSEH) examinations as it forms the foundational building block for Calculus and appears consistently in both objective and long-answer question formats, making it a high-scoring area if your conceptual clarity is strong.
Start Learning FreeKey Concepts
Reflexive Relation
A relation R on a set A is reflexive if every element relates to itself, meaning (a, a) is in R for all a in A.
Symmetric Relation
A relation R is symmetric if whenever (a, b) is in R, then (b, a) must also be in R for all a, b in A.
Transitive Relation
A relation R is transitive if whenever (a, b) and (b, c) are in R, then (a, c) must also be in 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 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 a pre-image in domain A, meaning range equals co-domain.
Important Formulas
Board Exam Info
In the Haryana Board (BSEH) Class 12 Mathematics exam, this chapter typically carries around 4 to 6 marks. Expect 1-mark multiple-choice questions or fill-in-the-blanks, a 2-mark short answer question checking reflexivity/symmetry, and a 4-mark or 5-mark long answer question asking to prove whether a given function is bijective or to prove an equivalence relation.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must separately prove three properties: Reflexive (show (a,a) belongs to R), Symmetric (show if (a,b) is in R then (b,a) is in R), and Transitive (show if (a,b) and (b,c) are in R then (a,c) is in R).
What is the easiest way to prove a function is one-one?
Assume two arbitrary elements x1 and x2 in the domain such that f(x1) = f(x2), and algebraically solve to show that x1 must equal x2.
Do I need to check both domain and co-domain when proving onto functions?
Yes! Always write down y = f(x), express x in terms of y, and verify that for every y in the co-domain, the resulting x belongs to the domain.
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