It is false that both Arthur is not anxious and Billy is not boisterous
If Xavier is difficult and Billy is boisterous then Penelope is a prude
If Xavier is not difficult then Arthur is anxious
Arthur is not anxious
Therefore, it is false that if Xavier is difficult then Penelope is not a prude.

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1. It is false that both Arthur is not anxious and Billy is not boisterous.
2. If Xavier is difficult and Billy is boisterous then Penelope is a prude.
3. If Xavier is not difficult then Arthur is anxious.
4. Arthur is not anxious.
5. Therefore, it is false that if Xavier is difficult then Penelope is not a prude.

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