Class 12 Maths - GUJARAT
Relations and Functions
The chapter 'Relations and Functions' builds upon foundational concepts learned in Class 11, introducing advanced topics crucial for Gujarat (GSEB) Class 12 board examinations. Students explore types of relations including reflexive, symmetric, transitive, and equivalence relations, alongside functions categorized as one-one (injective), onto (surjective), and bijective. The chapter also covers the composition of functions and invertible functions. Mastering this chapter is essential as it forms the basis for calculus and algebra, frequently appearing in board exam objective, short, and long-answer sections.
Start Learning FreeKey Concepts
Reflexive Relation
A relation R on 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 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) belong to R, which implies that (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 (Injective) Function
A function f: A -> B is one-one if distinct elements in A have distinct images in B, meaning f(x1) = f(x2) implies x1 = x2.
Onto (Surjective) Function
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 Gujarat (GSEB) Class 12 Mathematics board examination, Relations and Functions typically carries around 6 to 8 marks. Questions frequently include proving whether a given relation is an equivalence relation, checking the injectivity and surjectivity of specific functions, and finding the composite or inverse of functions.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must mathematically prove that the relation satisfies all three conditions: reflexivity, symmetry, and transitivity, usually using general variables from the given set.
What is the difference between domain, co-domain, and range?
The domain is the set of all possible input values, the co-domain is the entire set of possible output values, and the range is the actual set of outputs produced by the function.
Is every one-one function automatically onto?
No, a function can be one-one without being onto. For example, f: N -> N defined by f(x) = 2x is one-one but not onto because odd numbers in the co-domain have no pre-image.
Learn Relations and Functions with Your AI Tutor
10 different ways to study this chapter. Free for 3 chapters per day.
Lecture
Key Points
Interactive
Quiz
Flashcards