Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.1k views
in Sets, Relations and Functions by (49.9k points)
closed by

Let * be a binary operation on N given by a * b = 1 cm of a and b. Find the value of 20 * 16. Is * (i) commutative, (ii) associative?

1 Answer

+1 vote
by (48.6k points)
selected by
 
Best answer

We know that a * b = LCM of a and b

So 20 * 16 = LCM of 20 and 16 = 80

Commutative:

Consider a and b ∈ N

So LCM of a and b = LCM of b and a

Here, a * b = b * a Ɐ a and b ∈ N

Therefore, * is commutative.

Associative:

(a * b) * c = LCM of a and b * c

Here,

= LCM of {(LCM of a and b) and C} = LCM of {LCM of a, b and c}

We get

= LCM of (a and [LCM of b and c]) = a * (LCM of b and c)

So

= a * (b * c)

We can write it as

a * (b * c) = (a * b) * c Ɐ a, b ∈ c ∈ N.

Therefore, * is associative.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...