text: Discrete Mathematics with Graph Theory (3rd Edition) 29
  
  # Discrete Mathematics with Graph Theory (3rd Edition) 29 -...
  
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  Chapter 1 27 Together with ql, disjunctive syllogism gives (""Pl) V rl which is logically equivalent to Pl ---+ rl. Thus the given premises imply Pn ---+ rn which, again using 8(a), are logically equivalent to the single premise (pl ---+ rl) /\ (p2 ---+ r2) /\ ... /\ (pn ---+ rn). 10. [BB] In Latin, modus ponens means "method of affirming" and modus tollens means "method of denying". This is a reflection of the fact that modus tollens has a negative ...,p as its conclusion, while modus ponens affirms the truth of a statement q. Chapter 1 Review 1. P q r ...,r q ---+ (...,r) P /\ (q ---+ (...,r))
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  Unformatted text preview: ...,q (...,q) V r T T T F F F F T T T F T T T F F T F T F T T T T F T T F F F F T T F F T T T T T F T F T T F F F F F T F T F 'T T F F F T T F T T (p /\ (q ---+ (...,r))) ---+ ((. ..,q) V r) T F T T T T T T 2. We have. ..,r is F, so (...,r) /\ s is F. Since q is T, this means q ---+ ((. ..,r) /\ s) is F. Butp is T, so P V (q ---+ ((. ..,r) /\ s)) is T. Also r /\ t is T. Hence the entire statement has truth value T. 3. (a) A truth table shows this is a contradiction. P q ...,q ...,p P /\ (...,q) (. ..,p)Vq [p /\ (...,q)]/\ [(. ..,p) V q] T T F F F T F T F T F T F F F T F T F T F F F T T F T F...
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explanation: The text extract appears to be from a textbook on Discrete Mathematics with Graph Theory. It contains explanations and examples of logical reasoning, specifically discussing modus ponens and modus tollens, and includes a truth table and logical expressions. The extract does not contain a clear, direct question or a question-and-answer pair.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
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  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Discrete Mathematics with Graph Theory (3rd Edition) 29
  
  # Discrete Mathematics with Graph Theory (3rd Edition) 29 -...
  
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  Chapter 1 27 Together with ql, disjunctive syllogism gives (""Pl) V rl which is logically equivalent to Pl ---+ rl. Thus the given premises imply Pn ---+ rn which, again using 8(a), are logically equivalent to the single premise (pl ---+ rl) /\ (p2 ---+ r2) /\ ... /\ (pn ---+ rn). 10. [BB] In Latin, modus ponens means "method of affirming" and modus tollens means "method of denying". This is a reflection of the fact that modus tollens has a negative ...,p as its conclusion, while modus ponens affirms the truth of a statement q. Chapter 1 Review 1. P q r ...,r q ---+ (...,r) P /\ (q ---+ (...,r))
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  Unformatted text preview: ...,q (...,q) V r T T T F F F F T T T F T T T F F T F T F T T T T F T T F F F F T T F F T T T T T F T F T T F F F F F T F T F 'T T F F F T T F T T (p /\ (q ---+ (...,r))) ---+ ((. ..,q) V r) T F T T T T T T 2. We have. ..,r is F, so (...,r) /\ s is F. Since q is T, this means q ---+ ((. ..,r) /\ s) is F. Butp is T, so P V (q ---+ ((. ..,r) /\ s)) is T. Also r /\ t is T. Hence the entire statement has truth value T. 3. (a) A truth table shows this is a contradiction. P q ...,q ...,p P /\ (...,q) (. ..,p)Vq [p /\ (...,q)]/\ [(. ..,p) V q] T T F F F T F T F T F T F F F T F T F T F F F T T F T F...
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  • As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
  
  Kiran Temple University Fox School of Business ‘17, Course Hero Intern
  
  • I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
  
  Dana University of Pennsylvania ‘17, Course Hero Intern
  
  • The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
  
  Jill Tulane University ‘16, Course Hero Intern
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distilabel_metadata.raw_output_q_a_detector_0: The text extract appears to be from a textbook on Discrete Mathematics with Graph Theory. It contains explanations and examples of logical reasoning, specifically discussing modus ponens and modus tollens, and includes a truth table and logical expressions. The extract does not contain a clear, direct question or a question-and-answer pair.
  
  Label: no-question