Example 30 - Show subtraction, division are not binary on N - Examples

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
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Example 30 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

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.