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Concept Maps

Binary Operations — Concept Maps

ICSE · Class 12 · Mathematics

4 concept maps of Binary Operations for ICSE Class 12 Mathematics, each also written out as a text outline. Part of the ICSE Class 12 Mathematics syllabus.

101 questions30 flashcards5 formulas & key relations5 concepts

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4 Concept Maps

Decision tree to determine if an operation is binary based on closure property

Decision tree to determine if an operation is binary based on closure property

The map in words

  • Check if * is Binary Operation on Set A
    • Does a * b ∈ A for ALL a, b ∈ A?
      • Closure satisfied: YES - It is a Binary Operation
      • Closure fails: NO - It is NOT a Binary Operation

Step-by-step process to verify binary operations with closure law

Step-by-step process to verify binary operations with closure law

The map in words

  • Operation: a * b on Set A
    • Test: Pick ANY a, b from A
      • Is a * b in A?
        • YES for all pairs: ✓ Binary Operation
          • Closure law satisfied
        • NO for some pair: ✗ Not Binary Operation
          • Counterexample found

Test for commutativity with examples of commutative and non-commutative operations

Test for commutativity with examples of commutative and non-commutative operations

The map in words

  • Is a * b = b * a for ALL a, b ∈ A?
    • Check with examples and algebra
      • YES: ✓ COMMUTATIVE OPERATION
        • Addition, Multiplication, LCM, HCF
      • NO: ✗ NOT COMMUTATIVE
        • Subtraction, Division, Power function

Binary operations on a non-empty set and their properties

Binary operations on a non-empty set and their properties

The map in words

  • Binary operations on a non-empty set and their properties
    • Binary operation
    • Closure law
    • Commutative law
    • Associative law
    • Identity element
    • Invertible element
    • Inverse
    • Number 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.
What do the concept maps for Binary Operations show?
The 4 maps show how the ideas in Binary Operations connect: Decision tree to determine if an operation is binary based on closure property; Step-by-step process to verify binary operations with closure law. Each map is also written out as an outline on this page.
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.

More resources for Binary Operations

All ICSE Class 12 Mathematics Concept Maps

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