Reduction – Reaction in which a substance gains electrons. ... Oxidation cannot occur without reduction occurring at the same time. If one substance loses electrons then another substance has to gain those electrons.

Can oxidation and reduction occur alone?

No , alone oxidation or reduction can not take place , because if suppose one of the substance get oxidised by removing the electrons then other must be there to gain that electrons , so oxidation - reduction are complementary to each other , and these reactions are called Redox reactions.

Is it possible to have a reduction without an oxidation or an oxidation without a reduction Why or why not?

Nope. Oxidation occurs because an agent that causes the oxidation---the oxidizing agent---must itself get reduced. You may be confused as to what it means to have a half-reaction; in those, one atom or compound gets reduced or oxidized, but nothing else gets oxidized or reduced.