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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 :
Unless beggars are failures, wise men are not poor and money is not evil.

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To translate the statement "Unless beggars are failures, wise men are not poor and money is not evil" into symbols, we will follow these steps: ### Step-by-Step Solution: 1. **Identify the components of the statement:** - Let \( p \) represent "Money is evil." - Let \( q \) represent "Wise men are poor." - Let \( r \) represent "Beggars are failures." 2. **Negate the components:** - The negation of \( p \) (money is not evil) is \( \neg p \). - The negation of \( q \) (wise men are not poor) is \( \neg q \). - The negation of \( r \) (beggars are not failures) is \( \neg r \). 3. **Translate "Unless beggars are failures":** - The phrase "unless beggars are failures" can be logically interpreted as "if beggars are not failures." Thus, we can write this as \( \neg r \) implies the rest of the statement. 4. **Combine the components:** - The statement "wise men are not poor and money is not evil" can be expressed as \( \neg q \land \neg p \). 5. **Construct the final logical statement:** - Putting it all together, we have: \[ \neg r \implies (\neg q \land \neg p) \] ### Final Answer: The statement "Unless beggars are failures, wise men are not poor and money is not evil" can be translated into symbols as: \[ \neg r \implies (\neg q \land \neg p) \]
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