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Syllabus

Binary Operations — Syllabus

ICSE · Class 12 · Mathematics

What Binary Operations covers in ICSE Class 12 Mathematics: 4 topics, for the 2026-27 session. Part of the ICSE Class 12 Mathematics syllabus.

101 questions30 flashcards5 formulas & key relations5 concepts

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4 Topics · ICSE Class 12 Mathematics · 2026-27

Topics in Binary Operations

1

1. Meaning of a Binary Operation

  • A binary operation combines two elements of a set.
  • The result must belong to the same set.
  • The operation is written using symbols such as *, o, ⊗, and ⊕.
2

2. Number of Binary Operations on a Finite Set

  • If a finite set A has p elements, then A × A has p^2 elements.
  • The number of binary operations on A is p^(p^2).
  • For {1,2,3}, the number of binary operations is 3^9.
3

3. Commutative and Associative Laws

  • A binary operation is commutative if a * b = b * a for every a, b in A.
  • If * satisfies commutative law, A is said to be Abelian with respect to *.
  • A binary operation is associative if (a * b) * c = a * (b * c) for every a, b, c in A.
4

4. Identity Element and Inverse

  • An identity element e satisfies a * e = e * a = a for every a in A.
  • If an identity exists, it is always unique.
  • An element a is invertible if there exists b in A such that a * b = b * a = e.

Key Concepts

Central concept: Binary operations on a non-empty set and their properties

Binary operationClosure lawCommutative lawAssociative lawIdentity elementInvertible elementInverseNumber of binary operations on a finite set

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Frequently Asked Questions

What are the important topics in Binary Operations for ICSE Class 12 Mathematics?
Key topics in Binary Operations include Meaning of a Binary Operation, Number of Binary Operations on a Finite Set, Commutative and Associative Laws, Identity Element and Inverse. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How should I revise Binary Operations for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 101 practice questions on Binary Operations. 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 ICSE Class 12 Mathematics Syllabus

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