11. Let S(x) be the predicate "x is a student," F(x) the pred-icate "x is a faculty member," and A(x, y) the predicate"x has asked y a question," where the domain consists ofall people associated with your school. Use quantifiers toexpress each of these statements.a) Lois has asked Professor Michaels a question.b) Every student has asked Professor Gross a question.

Answered: Image /qna-images/answer/d7eb271b-6471-4d14-8dd0-45d970f4d4a2.jpg

Answered: . Let S(x) be the predicate "x is a…

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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DO NOT COPY FROM OTHER WEBSITES COrrect and detailed answer will be Upvoted else downvoted. Thank you!
. If the domain consists of all animals, express the following statements in terms of quantifiers and logical connectives, where B ( x ) = x is a bear, G ( x ) = x raids garbage cans, H ( x ) = x loves honey, and T ( x ) = lives in tents. A bear lives in a tent. Bears love honey. Only bears raid garbage cans. No bear lives in a tent. Some bears do not love honey.
8. Use quantifiers and predicates with more than one variable to express this statement: “There a person in your class who has taken every math class at Liberty University." Let the domain of x be all people and the domain of y be all classes.
21. Let the following predicates be given. The domain is all computer science classes. I(r) = "x is interesting." U(x) = "x is useful." H(x, y) = “x is harder than y." M(x, y) = “x has more students than y." (a) Write the following statements in predicate logic. i. All interesting CS classes are useful. ii. There are some useful CS classes that are not interesting. iii. Every interesting CS class has more students than any non- interesting CS class. (b) Write the following predicate logic statement in everyday English. Don't just give a word-for-word translation; your sentence should make sense. (3)[I(x) A (Vy)(H(x,y)→ M(y, x))] (c) Formally negate the statement from part (b). Simplify your negation so that no quantifier lies within the scope of a negation. State which derivation rules you are using. (d) Give a translation of your negated statement in everyday English.
Consider the sentences Vx3yP(x, y) and y\xP(x, y). Are these sentences true or false under the interpretation where x and y range over the positive integers and P(x, y) is "x divides y"? Vx³yP(x, y) is true, Vxy(x, y) is true, Vx³yP(x, y) is false, Vx³yP(x, y) is false, yvxP(x, y) is true yxP(x, y) is false y\xP(x, y) is true yvxP(x, y) is false
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The following statement is not a tautology. Find a counterexample. p V -q V (q→ p)

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