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CBSE Class 12-science Answered

Is the binary operation defined on set N, given a*b=a+b/2  is coomutative or associative  
Asked by niharikapabba2605 | 12 Oct, 2018, 01:48: PM
answered-by-expert Expert Answer
According to the question,
a*b = (a+b)/2
Operation is obviously commutative as a + b = b + a
To check for this operation is  associative or not
begin mathsize 16px style straight a asterisk times left parenthesis straight b asterisk times straight c right parenthesis equals straight a asterisk times open parentheses fraction numerator straight b plus straight c over denominator 2 end fraction close parentheses space space space space space space space space space space space space space space space space equals space fraction numerator straight a plus fraction numerator straight b plus straight c over denominator 2 end fraction over denominator 2 end fraction space space space space space space space space space space space space space space space space equals fraction numerator 2 straight a plus straight b plus straight c over denominator 4 end fraction........ left parenthesis straight i right parenthesis straight a asterisk times left parenthesis straight b asterisk times straight c right parenthesis space equals space open parentheses fraction numerator straight a plus straight b over denominator 2 end fraction close parentheses asterisk times straight c space space space space space space space space space space space space space space space space space equals space fraction numerator fraction numerator straight a plus straight b over denominator 2 end fraction plus straight c over denominator 2 end fraction space space space space space space space space space space space space space space space space space space equals space fraction numerator straight a plus straight b plus 2 straight c over denominator 4 end fraction......... left parenthesis ii right parenthesis From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space we space can space conclude space that space straight a asterisk times left parenthesis straight b asterisk times straight c right parenthesis space not equal to straight a asterisk times left parenthesis straight b asterisk times straight c right parenthesis Hence comma space the space given space operation space is space not space associative. end style
Answered by Sneha shidid | 12 Oct, 2018, 02:36: PM

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