Question 13 - Examples - Chapter 1 Class 12 Relation and Functions

Last updated at April 16, 2024 by

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

Example 30 - Chapter 1 Class 12 Relation and Functions - Part 2

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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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo