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

Let a, b `in` R
For addition
a,b `in ` R `implies ` a+b `in` R
`:. ` '+' is a binary operation on R.
For subtraction ,
`a,b in R implies a-b in R`
`:.` '-' is a binary operation on R.
For multiplication ,
`a, b in R implies a,b in R`
`:.` `'xx'` is a binary operation on R.
For division ,
`a, b in R implies (a)/(b) notin R, ` if b=0
`:.` `'div'` is not a binary operation on R.
Hence Proved.