Let \(P\) be the partial order defined on the set \(\{1, 2, 3, 4\}\) as follows:
\[
P = \{(x, x) \mid x \in \{1, 2, 3, 4\}\} \cup \{(1, 2), (3, 2), (3, 4)\}
\]
The number of total orders on \(\{1, 2, 3, 4\}\) that contain \(P\) is ...........\_\_\_.
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Solution and Explanation
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