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Let '*' be a binary operation on N given...

Let `'*'` be a binary operation on N given by `a*b=LdotCdotMdot(a , b)` for all `a , b in Ndot` Find `5*7,20*16` (ii) Is * commutative? Is * associative? Find the identity element in N Which element of N are invertible? Find them.

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i) Now `5 ** 7`= LCM of `5` and `7=35` again `20 ** 16`= LCM of `20` and `16=80.`
ii) Yes * is commutative, because `{a} * {b}={LCM} `of `{a}` and `{b}={LCM} `of` {b}` and `{a}={b} * a forall {a}, {b} in{N}.`
iii) Yes * is also associative, because `a *(b * c)=L C M of a, b, c=(a * b) * c for a, b, c in {N}.`
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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