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Show that addition, subtraction and mul...

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.

Text Solution

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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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Knowledge Check

  • Which of the following is not a binary operation on the indicated set?

    A
    On `Z^(+),**` defined by `a**b=a-b`
    B
    On `Z^(+),**` defined by `a**b=ab`
    C
    On `R,**` defined by `a**b=ab^(2)`
    D
    None of above

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