Questions: Let s represent "she sings for a living," let t represent "he fixes boats," and let r represent "they collect books." Express the compound statement in words. If he does not fix boats, then they collect books. What are the words that express the conditional statement? A. If he does not fix boats, then they collect books. B. If he does not fix boats, then they do not collect books. C. If they collect books, then he does not fix boats. D. If he fixes boats, then they collect books.

Let s represent "she sings for a living," let t represent "he fixes boats," and let r represent "they collect books." Express the compound statement in words. If he does not fix boats, then they collect books. What are the words that express the conditional statement? A. If he does not fix boats, then they collect books. B. If he does not fix boats, then they do not collect books. C. If they collect books, then he does not fix boats. D. If he fixes boats, then they collect books.
Transcript text: Let s represent "she sings for a living," let $t$ represent "he fixes boats," and let r represent "they collect books." Express the compound statement in words. \[ \sim t \rightarrow r \] What are the words that express the conditional statement? A. If he does not fix boats, then they collect books. B. If he does not fix boats, then they do not collect books. C. If they collect books, then he does not fix boats. D. If he fixes boats, then they collect books.
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Solution

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Solution Steps

Step 1: Identify Symbolic Representations
  • Symbol t represents the statement: "he fixes boats".
  • Symbol r represents the statement: "they collect books".
Step 2: Interpret Logical Operators
  • The logical operator used is negation (\(~\)) followed by implication (\(\rightarrow\)), forming a conditional statement of the form \(~X \rightarrow Y\).
Step 3: Translate to Natural Language
  • The symbolic logical statement translates to: "If not he fixes boats, then they collect books."

Final Answer:

The interpreted conditional statement is: "If not he fixes boats, then they collect books."

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