Example 3. Four singers, A, B, C, and D, participated in a competition, and one of them won. Someone interviewed these four singers.
A said: "I won."
B said: "A did not win, and C did not win either."
C said: "It's either A or B who won."
D said: "It's B who won."
Among the four singers' statements, two are correct. Please tell us: Which singer won?
\begin{tabular}{|l|l|l|l|l|}
\hline True $(1)$ or False $(0)$ & Jia & Yi & Bing & Ding's statement \\
\hline Jia, Jia wins & 1 & 0 & 0 & 0 \\
\hline Yi: Jia doesn't win, Bing doesn't win & 0 & 1 & 0 & 1 \\
\hline Bing, Jia wins or Yi wins & 1 & 1 & 0 & 0 \\
\hline Ding: Yi wins & 0 & 1 & 0 & 0 \\
\hline
\end{tabular}

From the table above, we see: In the Yi column, one statement is false, in the Bing column, all four statements are false, and in the Ding column, three statements are false. Only in the Jia column are two statements true, so Jia wins.