Class 12 Maths - KERALA
Relations and Functions
The chapter Relations and Functions builds upon the foundational concepts learned in Class 11, moving deeper into advanced mapping and pairing. Students in the Kerala SCERT Class 12 curriculum will explore types of relations including reflexive, symmetric, transitive, and equivalence relations, as well as functions that are one-one (injective), onto (surjective), and bijective. The chapter also covers the composition of functions and invertible functions. Mastering this chapter is crucial for board exams as it frequently contributes high-weightage questions, particularly 4-mark and 6-mark problems testing proofs of equivalence relations and invertibility.
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) 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 (a, b) and (b, c) being in R implies that (a, c) is also in R for all a, b, c in A.
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 in the domain have distinct images in the co-domain, so 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, meaning Range = Co-domain.
Important Formulas
Board Exam Info
In the Kerala (SCERT) Class 12 Mathematics public examination, this chapter typically carries around 6 to 8 marks. Common question types include checking whether a given relation is an equivalence relation, proving a function is bijective, and finding the composite or inverse of given functions.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must prove three things step-by-step: reflexivity (aRa), symmetry (if aRb then bRa), and transitivity (if aRb and bRc then aRc) using algebraic general forms, not just numbers.
What is the easiest way to prove a function is one-one?
Assume f(x1) = f(x2) for any two elements x1 and x2 in the domain, and solve algebraically to show that it ultimately simplifies to x1 = x2.
Do I need to find the range to prove onto?
Yes, for onto functions, you can either show that for every y in the co-domain there exists an x in the domain such that f(x) = y, or prove that the range equals the co-domain.
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