Q1 of 123 Page 3

Let ‘*’ be a binary operation on N defined by a*b = L.C.M(a,b) for all a,b∈N.

Find 2*4, 3*5, 1*6.

Given that * is an operation that is valid on all natural numbers ‘N’ and is defined by a*b = L.C.M(a,b)


According to the problem, binary operation given is assumed to be true.


Let us find the values of 2*4,3*5,1*6


⇒ 2*4 = L.C.M(2,4) = 4


⇒ 3*5 = L.C.m(3,5)


⇒ 3*5 = 3×5 = 15


⇒ 1*6 = L.C.M(1,6)


⇒ 1*6 = 1×6 = 6


The values of 2*4 is 4 , 3*5 is 15 and 1*6 is 6


More from this chapter

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9

The binary operation * defined on R×R → R is defined as a*b = 2a + b. Find (2*3)*4.

 10

Let * be a binary operation on N given by a*b = LCM(a,b) for all a,b∈N. Find 5*7.

 1

Let ‘*’ be a binary operation on N defined by a*b = L.C.M(a,b) for all a,b∈N.

Check the commutativity and associativity of ‘*’ on N.

 2

Determine which of the following binary operations are associative and which are commutative:

* on N defined by a*b=1 for all a,b N