Assignment:
Indicate which of the following statements about sets under the specified operations are true. For the ones that are false, provide one counter-example.
(a) The set of irrational numbers under addition forms an abelian group.
(b) The set of complex numbers under multiplication forms a group.
(c) The set of rational numbers under multiplication and addition forms a ring.
(d) The set of rational numbers under multiplication and addition does not form a field.
Provide complete and step by step solution for the question and show calculations and use formulas.