Question:
have you been involved on the switchboard long

Does it follow that "You have no experience with the switchboard, right? "?
Answer:
no

Question:
With new sports becoming popular on television (arena football, X Games, NASCAR), fans have more choices and less loyalty.

Does it follow that "no new sports are becoming popular on television"?
Answer:
no

Question:
'I'm sure I must have some around here somewhere.' He started rooting through my cupboards.

Does it follow that "He left the kitchen without touching anything."?
Answer:
no

Question:
I hope it's not egotistical of me to think that when I write an article for, say, the New Republic , I am not reaching nearly everyone who might have an interest in it.

Does it follow that "Everyone who might be interested in my writings is already reading them."?
Answer:
no