Question

If R+ denotes the set of positive real numbers, then determine whether the binary structure(R+,.) is a group. Solution. For each pair a,b in R+, the product ab is a unique positive real number. So R+, is closed under . , that is, . is a Question Blank 1 of 4 operation on . For all , we have so that is Question Blank 2 of 4 on . There exists such that for all . So, Question Blank 3 of 4 is the identity element of under . For each , there exists such that . So, Question Blank 4 of 4 is the inverse of in under . Hence is a group.

Name: if r denotes the set of positive real numbers then determine whether the binary structurer is a group solution for each pair ab in r the product ab is a unique positive real number so r is c 90473
Uploaded: 2023-03-29T18:14:08-08:00
Duration: 3 min 5 s
Channel: Aishwarya Krishnakumar
Description: if r denotes the set of positive real numbers then determine whether the binary structurer is a group solution for each pair ab in r the product ab is a unique positive real number so r is c 90473

          If  R+ denotes the set of positive real numbers, then determine whether the binary structure(R+,.)  is a group. 
Solution. For each pair a,b in R+, the product ab is a unique positive real number. So R+,  is closed under . , that is, . is a 
Question Blank 1 of 4
 operation on . 
For all , we have  so that  is 
Question Blank 2 of 4
 on . 
There exists  such that  for all . So,  
Question Blank 3 of 4
 is the identity element of under . 
For each , there exists such that . So, 
Question Blank 4 of 4
 is the inverse of in  under .
Hence  is a group.

Added by David F.

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