Determine whether `'+_6'` on `S={0,\ 1,\ 2,\ 3,\ 4,\ 5}` defined by `a+_6b={a+b ,\ if\ a+b<6a+b-6,\ if\ a+bgeq6` define a binary operation on the given set or not:

Explanation

Given `X={0,1,2,3,4,5}`
`a*b={{:(a+b,if a+b<6),(a+b-6 , if a+bge6):}`
To check if zero is the identify, we see that` a∗0=a+0=a`


for all `a∈x` and also `0∗a=0+a=a` for `a∈x`


Given `a∈X,a+0<6` and also `0+a<6`


`=>0` is the identity element for the given operation.


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