Discrete Math Question (Q 54 , P 38 , Textbook: Mathematical Structures for Comp

Question

Discrete Math Question (Q54, P38, Textbook: Mathematical Structures for Computer Science 7e):

Write the argument using propositional wffs (use the statement letters shown). Then, using propositional logic, prove that the argument is valid:

Either Emily was not home or if Pat did not leave the tomatoes, then Sophie was ill. Also, if Emily was not home, then Olivia left the peppers. But it is not true that either Sophie was ill or Olivia left the peppers. Therefore, Pat left the tomatoes and Olivia did not leave the peppers. E, P, S, O

Explanation / Answer

Ans-

Are these propositions? 1. The sun is shining. 2. The sum of two prime numbers is even. 3. 3+4=7 4. It rained in Austin, TX, on October 30, 1999. 5. x+y > 10 6. Is it raining? 7. Come to class! 8. n is a prime number. 9. The moon is made of green cheese. Definition: A propositional variable represents an arbitrary proposition. We represent propositional variables with uppercase letters. 1 What is an Argument? Definition: An argument consists of a sequence of statements called premises and a statement called a conclusion. An argument is valid if the conclusion is true whenever the premises are all true. Example: My program won’t compile or it produces a division by 0 error. My program does not produce a division by 0 error. Therefore my program will not compile. Now: Rewrite this argument in its general form by defining appropriate propositional variables. This is one example of an argument form that

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.