Class 12 Maths - WEST-BENGAL
Relations and Functions
The 'Relations and Functions' chapter in Class 12 Mathematics builds on Class 11 foundations, diving deeper into advanced mapping concepts. Students learn types of relations such as reflexive, symmetric, transitive, and equivalence relations, along with functions classified as one-one (injective), onto (surjective), and bijective. Additionally, the chapter covers the composition of functions and invertible functions. This foundational chapter is crucial for scoring high in the West Bengal Council of Higher Secondary Education (WBBSE) board exams, frequently appearing in both short-answer and long-answer question formats, and is essential for calculus.
Start Learning FreeKey Concepts
Reflexive Relation
A relation R on 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 whenever (a, b) and (b, c) belong to R, then (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 of 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 codomain B has at least one pre-image in the domain A.
Important Formulas
Board Exam Info
In the West Bengal (WBBSE) Class 12 Mathematics board examination, Relations and Functions typically carries around 4 to 6 marks. Common question types include checking whether a given relation is an equivalence relation, proving a function is bijective, and finding the inverse of a given invertible function.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must separately prove three properties: reflexivity, symmetry, and transitivity, by showing they hold true for all elements in the given set.
What is the difference between one-one and onto functions?
A one-one function ensures no two domain elements map to the same codomain element, while an onto function ensures no element in the codomain is left unmapped.
Do I need to find the range to prove a function is onto?
Yes, proving that the range of the function is equal to its given codomain is the standard method to show a function is onto.
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