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I Formalize the following statements, using the interpretation Sentence Letter Interpretation Pam is going. Quincy is going. R Richard is going.

I Formalize the following statements, using the interpretation Sentence Letter Interpretation Pam is going. Quincy is going. R Richard is going.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This is for my symbolic logic course. I need help with question 1.
### Supplementary Problems #### I. Formalize the following statements, using the interpretations indicated below: **Sentence Letter Interpretation:** - **P**: Pam is going. - **Q**: Quincy is going. - **R**: Richard is going. - **S**: Sara is going. **Statements:** 1. Pam is not going. 2. Pam is going, but Quincy is not. 3. If Pam is going, then so is Quincy. 4. Pam is going if Quincy is. 5. Pam is going only if Quincy is. 6. Pam is going if and only if Quincy is. 7. Neither Pam nor Quincy is going. 8. Pam and Quincy are not both going. 9. Either Pam is not going or Quincy is not going. 10. Pam is not going if Quincy is. 11. Either Pam is going, or Richard and Quincy are going. 12. If Pam is going, then both Richard and Quincy are going. 13. Pam is staying, but Richard and Quincy are going. 14. If Richard is going, then if Pam is staying, Quincy is going. 15. If neither Richard nor Quincy is going, then Pam is going. 16. Richard is going only if Pam and Quincy are staying. 17. Richard and Quincy are going, although Pam and Sara are staying. 18. If either Richard or Quincy is going, then Pam is going and Sara is staying. 19. Richard and Quincy are going if and only if either Pam or Sara is going. 20. If Sara is going, then either Richard or Pam is going, and if Sara is not going, then both Pam and Quincy are going.
Transcribed Image Text:### Supplementary Problems #### I. Formalize the following statements, using the interpretations indicated below: **Sentence Letter Interpretation:** - **P**: Pam is going. - **Q**: Quincy is going. - **R**: Richard is going. - **S**: Sara is going. **Statements:** 1. Pam is not going. 2. Pam is going, but Quincy is not. 3. If Pam is going, then so is Quincy. 4. Pam is going if Quincy is. 5. Pam is going only if Quincy is. 6. Pam is going if and only if Quincy is. 7. Neither Pam nor Quincy is going. 8. Pam and Quincy are not both going. 9. Either Pam is not going or Quincy is not going. 10. Pam is not going if Quincy is. 11. Either Pam is going, or Richard and Quincy are going. 12. If Pam is going, then both Richard and Quincy are going. 13. Pam is staying, but Richard and Quincy are going. 14. If Richard is going, then if Pam is staying, Quincy is going. 15. If neither Richard nor Quincy is going, then Pam is going. 16. Richard is going only if Pam and Quincy are staying. 17. Richard and Quincy are going, although Pam and Sara are staying. 18. If either Richard or Quincy is going, then Pam is going and Sara is staying. 19. Richard and Quincy are going if and only if either Pam or Sara is going. 20. If Sara is going, then either Richard or Pam is going, and if Sara is not going, then both Pam and Quincy are going.
**Logical Formula Assessment** **Task:** Determine which of the following formulas are well-formed formulas (wffs) and which are not. Explain your answer. 1. \(\sim (\sim P)\) 2. \(P \sim Q\) 3. \((P \leftrightarrow P)\) 4. \(P \rightarrow P\) 5. \(\sim \sim \sim (\sim P \& Q)\) 6. \(((P \rightarrow Q))\) 7. \(\sim (P \& Q) \& \sim R\) 8. \((P \leftrightarrow (P \leftrightarrow (P)))\) 9. \((P \rightarrow (Q = (R \& S)))\) 10. \((P = (Q \lor R \lor S))\) **Explanation:** - A well-formed formula (wff) in logic is one that is constructed according to the syntactic rules of the logical language. - Operators include negation (\(\sim\)), conjunction (\(\&\)), disjunction (\(\lor\)), implication (\(\rightarrow\)), and biconditional (\(\leftrightarrow\)). - Parentheses are used to clearly define the structure and precedence of operations.
Transcribed Image Text:**Logical Formula Assessment** **Task:** Determine which of the following formulas are well-formed formulas (wffs) and which are not. Explain your answer. 1. \(\sim (\sim P)\) 2. \(P \sim Q\) 3. \((P \leftrightarrow P)\) 4. \(P \rightarrow P\) 5. \(\sim \sim \sim (\sim P \& Q)\) 6. \(((P \rightarrow Q))\) 7. \(\sim (P \& Q) \& \sim R\) 8. \((P \leftrightarrow (P \leftrightarrow (P)))\) 9. \((P \rightarrow (Q = (R \& S)))\) 10. \((P = (Q \lor R \lor S))\) **Explanation:** - A well-formed formula (wff) in logic is one that is constructed according to the syntactic rules of the logical language. - Operators include negation (\(\sim\)), conjunction (\(\&\)), disjunction (\(\lor\)), implication (\(\rightarrow\)), and biconditional (\(\leftrightarrow\)). - Parentheses are used to clearly define the structure and precedence of operations.
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