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If p -= Money is evil, q -= Wise men are...

If p `-=` Money is evil, q `-=` Wise men are poor, r `-=` beggars are failures. Then translate the following statement into symbols :
A necessary condition for money to be evil is that beggars are failures.

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To translate the statement "A necessary condition for money to be evil is that beggars are failures" into symbols, we will follow these steps: ### Step-by-Step Solution: 1. **Identify the Statements**: - Let \( P \) represent "Money is evil". - Let \( Q \) represent "Wise men are poor". - Let \( R \) represent "Beggars are failures". 2. **Understand the Phrase "Necessary Condition"**: - The phrase "A necessary condition for A is B" can be translated into logical symbols as \( A \implies B \). This means that if \( A \) is true, then \( B \) must also be true. 3. **Apply the Necessary Condition to the Given Statement**: - In our case, we need to express that for money to be evil (which corresponds to \( P \)), beggars must be failures (which corresponds to \( R \)). - Therefore, we can write this as \( P \implies R \). 4. **Final Representation**: - The final symbolic representation of the statement "A necessary condition for money to be evil is that beggars are failures" is \( P \implies R \). ### Final Answer: The statement in symbols is \( P \implies R \). ---
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