Q1 Assertion with predicatesLet P be a set of people, C' be a set of classes, and D be a set of departments. Assume we aregiven the following predicates:Enrolled (Person, Class)Major (Person, Department)OfferedBy (Class, Department).Use the given predicates to assert the concept "some students are not taking any classes which areoutside their major" as a propositional formula with quantifiers.

We are given the following information. P: set of people, C: set of classes, D: set of departments.…

Answered: Let P be a set of people, C' be a set…

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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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!"
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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.
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).
Let P:I am in Bangalore..O: I love cricket. : then q -> plq implies p) is: O I love cricket Iam not in Bangalore O Ifl am in Bangalore then I love cricket O If I love cricket then I am in Bangalore The statement which is logically equivalent to A (and) B is * O -(A->-B) O An -B AB AA-B
2. Underline or circle the predicates in the following sentences: • Martians are from outer space. Gianna loves The Simpsons. Aristotle taught Alexander the Great. The Civil War lasted 4 years. • Every star shines brightly.
In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates: • P(z) : z was given the placebo • D(z) : z was given the medication • M(z): z had migraines Translate cach of the following statements into a logical expression. Then negate the expression by adding a negation operation to the beginning of the expression. Apply De Morgan's law until cach negation operation applices directly to a predicate and then translate the logical expression back into English. Sample question: Some patient was given the placebo and the medication. 3r (P(z) ^ D(z)) • Negation: ¬ar (P(z) ^ D(z)) Applying De Morgan's law: ¥z (¬P(z) V ¬D(z)) English: Every patient was either not given the placebo or not given the medication (or both).
Describe the following combined propositions as English sentences if s = heavy snow, c = flight canceled, and d=there are delays а. b. sAc c. d→ (s V c) → (d V c) e. sA (d V c) d. s-

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