# Ex 1.4, 6 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at Aug. 11, 2021 by Teachoo

Last updated at Aug. 11, 2021 by Teachoo

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 *

Ex 1.4

Ex 1.4 ,1 (i)
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Ex 1.4 ,1 (ii) Important Deleted for CBSE Board 2022 Exams

Ex 1.4 ,1 (iii) Deleted for CBSE Board 2022 Exams

Ex 1.4 ,1 (iv) Important Deleted for CBSE Board 2022 Exams

Ex 1.4 ,1 (v) Deleted for CBSE Board 2022 Exams

Ex 1.4, 2 (i) Important Deleted for CBSE Board 2022 Exams

Ex 1.4, 2 (ii) Deleted for CBSE Board 2022 Exams

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Ex 1.4, 2 (iv) Important Deleted for CBSE Board 2022 Exams

Ex 1.4, 2 (v) Deleted for CBSE Board 2022 Exams

Ex 1.4, 2 (vi) Important Deleted for CBSE Board 2022 Exams

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Ex 1.4, 6 Important Deleted for CBSE Board 2022 Exams You are here

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Ex 1.4, 9 (iv) Important Deleted for CBSE Board 2022 Exams

Ex 1.4, 9 (v) Important Deleted for CBSE Board 2022 Exams

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Chapter 1 Class 12 Relation and Functions (Term 1)

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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.