Jacob4Jesus: I think in the first diagram is a mistake. If is played here then can only be here and secures three eyes.
symplicity: Count how many liberties each of black's groups have after . Because can do something different.
stoned: would be at a, removing the upper group of stones, so all of black dies.
Wind What about this?
ajisubarashii Black would reply at , capturing two white stones. Then the only way White can make progress is to play at , as otherwise Black plays at himself and makes two eyes. After White's , Black captures with . Then a and b are miai for Black to live.