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Chapter 1 Class 12 Relation and Functions
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Ex 1.4, 6 - Let a * b = LCM of a and b. Find 5 * 7, 20 * 16

Ex 1.4, 6 - Chapter 1 Class 12 Relation and Functions - Part 2
Ex 1.4, 6 - Chapter 1 Class 12 Relation and Functions - Part 3 Ex 1.4, 6 - Chapter 1 Class 12 Relation and Functions - Part 4 Ex 1.4, 6 - Chapter 1 Class 12 Relation and Functions - Part 5 Ex 1.4, 6 - Chapter 1 Class 12 Relation and Functions - Part 6


Transcript

Ex 1.4, 6 Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find 5 * 7, 20 * 16 5 * 7 = L.C.M. of 5 and 7 = 35 20 * 16 = L.C.M of 20 and 16 = 80 Ex 1.4, 6 Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find (ii) Is * commutative? Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ N * is commutative a * b = LCM of a & b b * a = LCM of b & a Ex 1.4, 6 (iii) Is * associative? Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b ∈ N * is associative (a * b)* c = (LCM of a & b) * c = LCM of (LCM of a & b) & c = LCM of a, b & c a * (b * c) = a * (LCM of b & c) = LCM of a & (LCM of b & c) = LCM of a, b & c Ex 1.4, 6 Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find (iv) Find the identity of * in N e is the identity of * if a * e = e * a = a i.e. LCM of a & e = LCM of e & a = a Let e = 1 L.C.M. of a & 1 = a L.C.M. of 1 & a = a ∴ a * 1 = 1 * a = a for all a ∈ N Thus, 1 is the identity of * in N. Ex 1.4, 6 Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find (v) Which elements of N are invertible for the operation * An element a in N is invertible if, there is an element b in N such that , a * b = e = b * a Here, b is the inverse of a Here, e = 1 So, a * b = 1 = b * a i.e. LCM of a & b = 1 = LCM of b & a LCM of two numbers are 1 if both numbers are 1 So, a = b = 1 Hence, 1 is the only invertible element in N for operation *

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.