Let `S=(0,1,2,3,4,)` and * be an operation on S defined by `a*b=r` , where`r` is the least non-negative remainder when `a+b` is divided by 5. Prove that * is a binary operation on S.

Explanation

`a` * `b sub S Rightarrow `* is a binary operation on s


`0^{**} 0=(0+0) %5)=0 `

`0^{**}1=((0+1) % cdot 5)=1 `

`0 ^{**} 2=((0+2) % 5)=2 `

`2^{**} 3=((2+3) % 5)=0 `

`3^{**} 4=((3+4) % 5)=2`

`{0,1,2,3,4} sub S`

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