Question

Which of the following are binary operations on `S={x∈R|x>0}`? Justify your answer. (i)The operations `∇` is defined by `x∇y=|ln(xy)|` where `lnx` is a natural logarithm. (ii) The operations `∆` is defined by `x∆y=x^2+y^3`.

Answer 1

They are both binary operations. See explanation.

Explanation:

An operation (an operand) is binary if it requires two arguments to be calculated.

Here both operations require 2 arguments (marked as `x` and `y`), so they are binary operations.