Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary operation on R. Further, show that division is a binary operation on the set R of nonzero real numbers.

Explanation

Addition

`+:RtimesR ->R`

and `(a,b)->a+b`

for every real number a and b, ` a+b` is also real.

`:.` `+` is a binary operation on R.



Subtraction

`-` `:RtimesR->R`

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