$5)$ The following criteria have all been suggested and$/$or utilized as diagnostics for whether a polymerization is living or not. For each one, explain why it might be useful, and then decide whether or not it is a robust criterion, that is$,$ can you think of a situation in which the criterion is satisfied but the polymerization is not living?

a$)$ Polymerization proceeds until all monomer is consumed. Polymerization continues if more monomer is then added.

b$)$ The number of polymer molecules is constant, and independent of conversion.

c$)$ Narrow molecular weight distributions are produced.

d$)$ The concentration of monomer decreases to zero, exponentially with time.