Example 4 If $\bar{B} \Rightarrow \bar{A}$ holds, and $\bar{A} \Rightarrow \bar{B}$ does not hold, then condition $B$ is ( ) for conclusion $A$ to hold.
(A) Sufficient but not necessary condition
(B) Necessary but not sufficient condition
(C) Sufficient and necessary condition
(D) Neither sufficient nor necessary condition
Solution: From “$\bar{B} \Rightarrow \bar{A}$ holds,” we get “$B \Leftarrow A$ holds.” From “$\bar{A} \Rightarrow \bar{B}$ does not hold,” we get “$A \Leftarrow B$ does not hold.” That is, condition $B$ is a necessary but not sufficient condition for conclusion $A$. Choose B.

Key to Solving: Implication relationships are important tools for judging necessary and sufficient conditions, and their essence is to determine the truth or falsity of the four forms of a proposition.