Question

Which of the following are binary operations on S = {x ∈ R | x > 0}? Justify your
answer.
i) The operation Δ defined by xΔy = x(y− 2).
ii) The operation ∇ defined by x∇y = e^x+y.
Also, for those operations which are binary operations, check whether they are
associative and commutative.