Answer to Question #81130 in Linear Algebra for Ra

Question

Which of the following are binary operations on S = {x ∈ R | x > 0}? Justify your answer. i) The operation defined by xy=|ln(xy)| where lnx is the natural logarithm. ii.)The operation ∆ defined by x∆y=x2+y3. Also, for those operations which are binary operations, check whether they are associative or commutative.