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Question 13 - Binary Operations - Definition - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
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Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Question 13 Show that subtraction and division are not binary operations on N. Subtraction – : N × N → N where (a, b) → a – b Here, a & b are natural numbers (i.e. 1, 2, 3, 4, 5, …..) Let a = 3 & b = 5 a – b = 3 – 5 = –2 But –2 is not a natural number Hence, – is not a binary operation on N Division ÷ : N × N → N where (a, b) → a ÷ b Here, a & b are natural numbers (i.e. 1, 2, 3, 4, 5, …..) a ÷ b = 𝑎/𝑏 Let a = 3 & b = 5 𝑎/𝑏 = 3/5 But 𝟑/𝟓 is not a natural number Hence, ÷ is not a binary operation on N
