




Introducing your new favourite teacher - Teachoo Black, at only ₹83 per month
Miscellaneous
Misc 2
Misc 3 Important
Misc. 4 Important
Misc 5
Misc 6
Misc 7
Misc. 8 Important
Misc 9 Important Deleted for CBSE Board 2023 Exams
Misc 10 Important
Misc 11 (i) Important
Misc 11 (ii)
Misc 12 Deleted for CBSE Board 2023 Exams You are here
Misc 13 Important
Misc 14 Important Deleted for CBSE Board 2023 Exams
Misc 15
Misc 16 (MCQ) Important
Misc 17 (MCQ) Important
Misc 18
Misc 19 (MCQ) Important
Last updated at May 29, 2018 by Teachoo
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 *