# Misc 12 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 12 Consider the binary operations * : R × R → and o : R × R → R defined as a * b = a – b and a o b= a, ∀ a, b ∈ R. Show that * is commutative but not associative, o is associative but not commutative. Further, show that ∀ a, b, c ∈ R, a * (b o c) = (a * b) o (a * c). (If it is so, we say that the operation * distributes over the operation o). Does o distribute over *? Justify your answer. Check commutative for * * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ R * is commutative Check associative for * * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not associative a o b = a Check commutative for o o is commutative if a o b = b o a Since a o b ≠ b o a * is not commutative Check associative for o o is associative if (a o b) o c = a o (b o c) Since (a o b) o c = a o (b o c) o is not associative a * b = a – b & a o b = a * distributes over o If a * (b o c) = (a * b) o (a * c), ∀ a, b, c ∈ R * distributes over o Since a * (b o c) = (a * b) o (a * c), ∀ a, b, c ∈ R * distributes over o a * b = a – b & a o b = a o distributes over * If a o (b * c) = (a o b) * (a o c), ∀ a, b, c ∈ R o distributes over * Since a o (b * c) ≠ (a o b) * (a o c) o does not distributes over *

Miscellaneous

Misc 1
Deleted for CBSE Board 2022 Exams

Misc 2 Deleted for CBSE Board 2022 Exams

Misc 3 Important Deleted for CBSE Board 2022 Exams

Misc. 4 Important

Misc 5

Misc 6 Deleted for CBSE Board 2022 Exams

Misc 7 Deleted for CBSE Board 2022 Exams

Misc. 8 Important

Misc 9 Important Deleted for CBSE Board 2022 Exams

Misc 10 Important

Misc 11 (i) Important Deleted for CBSE Board 2022 Exams

Misc 11 (ii) Deleted for CBSE Board 2022 Exams

Misc 12 Deleted for CBSE Board 2022 Exams You are here

Misc 13 Important Deleted for CBSE Board 2022 Exams

Misc 14 Important Deleted for CBSE Board 2022 Exams

Misc 15

Misc 16 (MCQ) Important

Misc 17 (MCQ) Important

Misc 18 Deleted for CBSE Board 2022 Exams

Misc 19 (MCQ) Important Deleted for CBSE Board 2022 Exams

Chapter 1 Class 12 Relation and Functions (Term 1)

Serial order wise

About the Author

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.