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Sets, Relations and Functions — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Sets, Relations and Functions revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 4 topics in quick points.

49 questions30 flashcards11 formulas & key relations5 concepts

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Key Topics to Revise

1

Sets and Cartesian Product

  • A set is a well-defined collection of distinct objects.
  • Order of elements in a set does not matter and no element repeats.
  • Standard notations: N (natural numbers), Z (integers), Q (rational), R (real), C (complex).
2

Relations and Functions

  • A relation from set A to B is any subset of A × B.
  • Domain of a relation is the set of all first elements of its ordered pairs.
  • Range is the set of all second elements; codomain is the full set B.
3

Types of Functions

  • One-One (Injective): Different inputs give different outputs.
  • Onto (Surjective): Every element in codomain is mapped to by some element in domain.
  • Bijective: Both one-one and onto; has an inverse function.
4

Function Operations and Inverses

  • Composition of functions: (fog)(x) = f(g(x)) — apply g first, then f.
  • Order matters: fog ≠ gof in general.
  • Inverse function f⁻¹ exists only if f is bijective (one-one and onto).

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Full Notes

Key Concepts

A set is a wellThe Cartesian product of two setsA relation from set AFunctions can be classified based onA function f(x) is even if

Frequently Asked Questions

What are the important topics in Sets, Relations and Functions for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Sets, Relations and Functions include Sets and Cartesian Product, Relations and Functions, Types of Functions, Function Operations and Inverses. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Sets, Relations and Functions for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 49 practice questions on Sets, Relations and Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Telangana Open School (TOSS) Class 12 Mathematics Revision Notes

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