Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let * be a binary operation on the set Q of rational numbers as follows: a * b = ab over 4

Q. 9 Let ∗ be a binary operation on the set Q of rational numbers as follows:

(v) 

a * b = \frac{ab}{4}

Find which of the binary operations are commutative and which are associative.

Answers (1)

best_answer

On the set Q ,the operation * is defines as  a * b = \frac{ab}{4} .It is observed that:

For a,b \in Q

a * b = \frac{ab}{4}

b* a = \frac{ba}{4}

\therefore       a*b = b* a   for a,b \in Q 

Hence, the * operation is commutative.

It can be observed that

(a*b)*c =(\frac{ab}{4})*c = \frac{\frac{ab}{4}c}{4}=\frac{abc}{16}

a*(b*c) =a*(\frac{bc}{4}) = \frac{\frac{bc}{4}a}{4}=\frac{abc}{16}

  (a*b)*c = a*(b*c)  for all a,b,c \in Q

The operation * is 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

No changes in exam, IA system: CBSE rebuts claims of syllabus reduction, open book exams in 2025
anam-khan

Fact-check: CBSE hasn't reduced syllabus by 15%, internal assessments will not be 40% of score in 2025
anam-khan

CBSE date sheet 2025 for Classes 10, 12 likely in November last week: Reports

Latest Question