Class 12 Maths - ODISHA
Relations and Functions
The 'Relations and Functions' chapter in Class 12 Mathematics builds upon foundational concepts from Class 11, moving into more advanced ideas essential for the Odisha Board (BSE) examinations. Students learn to classify various types of relations such as reflexive, symmetric, transitive, and equivalence relations. The chapter also deepens the understanding of functions, focusing on one-one (injective), onto (surjective), and bijective functions, alongside the concept of invertible functions and binary operations. Mastery of this chapter is crucial as it forms the bedrock for calculus and algebra, frequently appearing in both objective and long-answer board exam questions.
Start Learning FreeKey Concepts
Reflexive Relation
A relation R on a 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 on a set A 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 on a set A is transitive if whenever (a, b) and (b, c) belong to R, then (a, c) must also belong 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, meaning 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 equals co-domain.
Important Formulas
Board Exam Info
In the Odisha (BSE) Class 12 Mathematics board examination, this chapter typically carries around 6 to 8 marks. Questions usually include 1-mark objective/multiple-choice questions, 2-mark short answer questions on checking equivalence relations or injectivity/surjectivity, and 4-mark long answer questions involving invertibility and composite functions.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must systematically prove three separate conditions: show it is reflexive for all elements, symmetric for any pair, and transitive for any triplet using algebraic definitions.
What is the difference between range and co-domain in functions?
The co-domain is the entire set B given in the function definition f: A -> B, while the range is the actual set of output images obtained by substituting all values of domain A into f(x).
Is every one-one function automatically onto?
No, a function can be one-one without being onto. For example, f: N -> N defined as f(x) = 2x is one-one but not onto because odd numbers in the co-domain have no pre-image.
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