23. Translate in two ways each of these statements into logi-cal expressions using predicates, quantifiers, and logicalconnectives. First, let the domain consist of the studentsin your class and second, let it consist of all people.a) Someone in your class can speak Hindi.b) Everyone in your class is friendly.c) There is a person in your class who was not born inCalifornia.d) A student in your class has been in a movie.e) No student in your class has taken a course in logicprogramming.

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Answered: 23. Translate in two ways each of these…

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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Explain what are the differences, if any, between a structure of L₂ (the language of predicate logic) and a structure of L (the language of predicate logic with identity).
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
Translate the statements into symbols. (Let p: Dinner includes soup; d: Dinner includes salad; v: Dinner includes the vegetable of the day.) (a) Dinner includes soup and salad, or the vegetable of the day, 16ASVY Op^ (dvv) Opvdvv 765950 Opv (dav)
Let M(x,y) be the predicate "person x has seen movie y," where the domain for x is the set of all people and the domain for y is the set of all movies. Express the following English sentence as a symbolic proposition: "There is a movie that has not been seen by any people." x-M(x,y) ⒸyVx-M(x, y) x-M(x,y) yx M(x,y) -
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.
Using the following translation key, translate each of the sentences of English, (i)-(vi), into PL.P: There is alien lifeQ: Humans are the only intelligent lifeformsR: Dogs are intelligentS: God existsT: Humans evolved(i) Either God exists and humans are the only intelligent lifeforms, or God doesn’t exist and there is alien life(ii) There is alien life only if God doesn’t exist(iii) Humans are the only intelligent lifeforms unless either there is alien life or dogs are intelligent(iv) God doesn’t exist just in case both humans evolved and they are the only intelligent lifeforms(v) If God exists and humans evolved, then if God exists then humans are not the only intelligent lifeforms
Translate the following sentence in terms of predicates, quantifiers, and logical connectives. Choose your own variables and predicate statement symbols as needed and define each of them clearly. Specify the domain
Paraphrase the following into quantificational notation: (a) If any student taking Logic cheats, then every student taking Logic will be unhappy. (b) If any student taking Logic cheats, then he or she will be unhappy. (c) Logic students are either clever or happy. (d) If anything is both gaseous and liquid, then it is a plasma. (e) No plasma is a liquid unless some plasma is a gas.
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).
Exercise 1. Express the following statements symbolically using multiple quantifiers. De- fine your domains and two-variable predicates. Then negate the statements. (a) Every rational number when multiplied by some integer is an integer. Domain(s): • Predicate: • Statement: • Negation: ● Englsih translation of negation: . Which is true? The original statement or its negation? Justify your answer.
Let p: you see lightning and q: you hear thunder. Write each of the following statements in symbolic notation: a. If you see lightning, then you hear thunder. b. If you hear thunder, then you see lightning.. c. If you don't see lightning, then you don't hear thunder. d. If you don't hear thunder, then you don't see lightning.. If you see lightning, then you hear thunder. If you hear thunder, then you see lightning If you don't see lightning, then you don't hear thunder If you don't hear thunder, then you don't see lightning 114 114 #p-q =q-p
Put the following predicate calculus expression in clause form: ∀X [odd(X) ⇔ [∀Y odd(mul(X,Y))]]

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