Let P(x) be the statement "x is happy" and Q(x) be the statement "x is under20", where the universe of discourse for x is the set of AOUstudents. Express each of the following English statement in terms ofquantifiers and logical connectives:i. There is an AOU student who is happy and over 20.ii. Not all AOU students are either unhappy or under 20.

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Answered: Let P(x) be the statement "x is happy"…

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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Express this in predicate logic: Each email address has exactly one email box. M(x): x is an email address B(x,y): x has an email box y
Given the domains m e MOVIES and ce CHARACTERS and the following predicates: • sW(m): m is a Star Wars movie. A(c, m): c is a character who appears in the movie m • D(c): c is a Droid. • L(m): I liked m. • Q(c, q): c says q (e is quoted as saying q.) • jarjar is the character Jar Jar Binks • bad is the quote: "I've got a bad feeling about this!"
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.
The rule of inference that permits us to derive a specific instance from a universal statement is A.Existential Generalization.B. Existential Instantiation.C. Universal Generalization.D. Universal Instantiation.
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.
3. How to express the associativity of V as a tautology?
Using relational predicates ( e.g. F(s,m) for, say, s can fool m), translate the following sentences into predicate logic. You can use English words for the quantification symbols (such as For All x instead of v x) if necessary Also give the negatives of each sentence in English. a) Everybody can fool somebody b) There is no-one who can fool everyone. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
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