Arizona State University MAT 243 Week1_Written Homework-QUESTIONS WITH VERIFIED ANSWERS

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1. Is ”Johann Sebastian Bach is the greatest of all the Baroque composers” a proposition? Explain. B(x): Johann Sebastian Bach G(x): Greatest C(x): Baroque composer x(B(x)C(x)) 2. Writ... e the negation of ”Hikaru is taller than Yutaka”. Your (verbally given) negation must not contain any words or phrases that explicitly express negation, such as ”not”, ”it is untrue that”, ”is false”, ”is incorrect”, etc. Yukata is at most as tall as Hikaru. 3. Write the fully simplified negation of 3 < x ≤ 4. The statement 3 ≤ � < 4 means 3 ≤ � and � < 4. By De Morgan, the negation of that is 3 > � or � ≥ 4. Symbolically, we can also write this as � < 3 ∨ � ≥ 4. 4. Is the conditional statement ”If a human being has 7 heads, then they have 11 arms” true or false? Explain. This is false because this statement is missing the necessary or sufficient words. 5. Rephrase in standard”if.. then” form: ”We are buying a new TV only if the old TV breaks down. If the old TV breaks down, then we are buying a new TV. 6. Rephrase in standard ”if.. then” form: ”In the United States, a good credit score is necessary for obtaining a loan.” If you are obtaining a loan in the United States, then you must have a good credit score. 7. Rephrase in contrapositive form: ”If you are taller than 6 ft, then it is unpleasant for you to travel in economy class.” Your contrapositive must not contain explicit references to negation. Assume that the negation of ”unpleasant” is ”pleasant”. If you are not taller than 6 ft, then it is pleasant for you to travel in economy class. 8. Give a logically equivalent expression to ¬p → q that does not use the conditional. Justify your answer. (pq) [Show More]

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