Ex 1.4, 9 - Find associative, commutative - Chapter 1 Class 12 - Ex 1.4

Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 2
Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 3 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 4 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 5 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 6 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 7 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 8 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 9 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 10 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 11 Ex 1.4, 9 - Chapter 1 Class 12 Relation and Functions - Part 12

  1. Chapter 1 Class 12 Relation and Functions (Term 1)
  2. Serial order wise

Transcript

Ex 1.4, 9 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : • a * b = a − b Check commutative * is commutative if a * b = b * a Since a * b ≠ b * a * is not commutative Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation Ex 1.4, 9 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (ii) a * b = a2 + b2 Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ Q * is commutative Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation Ex 1.4, 9 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (iii) a * b = a + ab Check commutative * is commutative if a * b = b * a Since a * b ≠ b * a * is not commutative a * b = a + ab Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation Ex 1.4, 9 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (iv) a * b = (a – b)2 Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ Q * is commutative Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation Ex 1.4, 9 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (v) a * b = ab﷮4﷯ Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ Q * is commutative Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b, c ∈ Q * is an associative binary operation Ex 1.4, 9 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (vi) a * b = ab2 Check commutative * is commutative if a * b = b * a Since a * b ≠ b * a * is not commutative Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.