Show that ∗:R×R→R given by (a,b)→a+4b2 is a binary operation.
Given: ∗:R×R→R given by (a,b)→a+4b2
For every real number a & b, a+4b2 is also a real number. Hence, ∗ is a binary operation on R.
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.