Class 12 Maths - ANDHRA-PRADESH
Relations and Functions
The Chapter 'Relations and Functions' in Class 12 Mathematics for Andhra Pradesh (BSEAP) builds upon the foundational concepts of sets learned in earlier classes. It delves deeper into types of relations such as reflexive, symmetric, transitive, and equivalence relations. Students also study various types of functions including one-one (injective), onto (surjective), and bijective functions, along with the composition of functions and invertible functions. Mastering this chapter is crucial for board exams as it forms the basis for calculus and algebra, frequently appearing in both short-answer and long-answer sections of the AP Board question paper.
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 for all a, b, c in A.
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 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 codomain B has at least one pre-image in the domain A, meaning range equals codomain.
Important Formulas
Board Exam Info
In the Andhra Pradesh (BSEAP) Class 12 Mathematics board examination, this chapter typically carries around 6 to 8 marks. Questions usually include verifying whether a given relation is an equivalence relation (often a 4-mark or 7-mark question) and proving injectivity and surjectivity of functions.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must separately prove that the relation satisfies all three properties: Reflexive, Symmetric, and Transitive, using general algebraic variables for elements in the set.
What is the easiest way to check if a function is one-one?
Assume f(x1) = f(x2) and solve to show that x1 must equal x2. Alternatively, check if the first derivative of the function is strictly increasing or decreasing throughout its domain.
Is fog always equal to gof?
No, the composition of functions is generally not commutative. fog(x) and gof(x) are usually different unless the functions are specifically defined to commute.
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