Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • For each operation star defined below, determine whether star is binary, commutative or associative. On R - {- 1}, define a * b = a over b + 1

Q.2 For each operation ∗ defined below, determine whether ∗ is binary, commutative
or associative.

(vi) On R - \{-1 \}, definea * b = \frac{a}{b +1}

Answers (1)

best_answer

(iv) On R - \{-1 \}, definea * b = \frac{a}{b +1}

 

         1\ast 2 = \frac{1}{2+1}=\frac{1}{3}         and      2\ast 1 = \frac{2}{2+1}= \frac{2}{3}

             \Rightarrow               1\ast 2\neq 2\ast 1       for 1,2 \in R - \{-1 \}

            \therefore  the operation is not commutative.

         (1\ast 2)\ast 3 = (\frac{1}{2+1}) \ast 3 = \frac{1}{3} \ast 3 = \frac{\frac{1}{3}}{3+1}= \frac{1}{12}

            1\ast (2\ast 3) = 1 \ast (\frac{2}{3+1}) = 1 \ast \frac{2}{4} = 1 \ast \frac{1}{2} = \frac{1}{\frac{1}{2}+1} = \frac{2}{3}

              \therefore             (1\ast 2)\ast 3\neq 1\ast (2\ast 3) ;     where 1,2,3 \in R - \{-1 \}

\therefore  operation * is not associative.   

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 Chemistry Exam Analysis 2025: Paper 'moderately difficult' but well balanced
anam-khan

CBSE Class 12 board exam still once a year; 20 lakh expected to appear in 2026 from February 17
anam-khan

CBSE board exams twice a year from 2025-26; 2 subject groups, 'better of two marks' in draft policy

Latest Question