2006b question 2

The answer is c.

Answer c states that for DFA A with "a" states and DFA B with b states, there doesn't exist a DFA which accepts A union B and has O(a+b) states.

Consider this example which contradicts answer c:

A and B accepts the same language, so there definitely exists a DFA with O(a+b) states, specifically min(a,b) states.

Could you please clarify why this does not contradict answer c.

2007a question 9

The answer is e.

Could you please clarify why answer c is incorrect, it seems that the pumping lemma application described in the answer is correct. Maybe except for the "for all n" part where it should be a pumping constant

Thanks in advanced.