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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 :
That beggars are failures is a sufficient condition that money is evil.

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To translate the statement "That beggars are failures is a sufficient condition that money is evil" into symbols using the given definitions, we can 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 Sufficient Condition**: - The phrase "A is a sufficient condition for B" can be expressed in logical terms as \( A \implies B \). This means if A is true, then B must also be true. 3. **Assign A and B**: - In our case, we need to identify which part corresponds to A and which corresponds to B in the statement "That beggars are failures is a sufficient condition that money is evil". - Here, "Beggars are failures" corresponds to A, which is represented by \( r \). - "Money is evil" corresponds to B, which is represented by \( p \). 4. **Translate the Statement**: - Since "Beggars are failures" (A) is a sufficient condition for "Money is evil" (B), we can write this as: \[ r \implies p \] ### Final Answer: The translated statement into symbols is: \[ r \implies p \]
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