wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

For given binary operation defined below, determine whether is binary, commutative or associative.
(iii)On Q, define ab=ab2

Open in App
Solution

On Q, define ab=ab2
ab2Q, so the operation is binary. It is known that
ab =ba for a,bQ
Therefore, ab2=ba2 for a,bQ
Therefore, ab=ba for a, bQ
Therefore, the operation is commutative.
For all a,b,cQ, we have
(ab)c=(ab2)c=(ab2)c2=abc4a(bc)=a(bc2)=a(bc2)2=abc4
Therefore,(ab)c=a(bc)
Therefore, the operation is associative.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Binary Operations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon