3.Let S(x) be the statement “x is a student," P(x) be the statement “x is aprofessor," and Q(x, y) be the statement “x asked a question to y." If the domain of x and yconsists of all people, express each of the following sentences in terms of S(x), P(x), Q(x,y),quantifiers, and logical operators.Example: Some student has asked every professor a question.Answer.3x(S(x) A Vy(P(V) → Q(x,y)))a. Every professor has been asked a question by some student.b. There is a student who has never asked a question to a professor.c. There is a professor who has been asked a question by exactly one student.d. There are two different students who have asked each other a question.

Let S(x) be the statement"x is a student,"P(x) be the statement"x is a professor," andQ(x, y) be the…

Answered: 3. Let S(x) be the statement “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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For "x is in A intersect B" give an equivalent statement that uses "x is in A" and "x is in B". You may use Java's notation for the boolean operators, and "is in" for set membership.
Proficiency #8. Which of the following are logically equivalent to the statement -[(Vx E U) (¬p(x) V q(x))] if U is the set of all parrots, p(x) is the statement "x is talkative", q(x) is the statement “x is green" (Choose all that apply): I. There is an parrot who is not green and is talkative. II. No talkative parrots are green. III. All green parrots are talkative. IV. Not all parrots are not green. V. At least one talkative parrot is not green. VI. Not all talkative parrots are green.
9. Let P(x) be the statement "x can speak Russian" and let Q(x) be the statement "x knows the computer language C++." Express each of these sentences in terms of P(x), Q(x), quantifiers, and logical connectives. The domain for quantifiers consists of all students at your school.
Which of the following is a logical equivalence in first-order logic? A. ¬(∀x)P(x) ≡ (∃x)¬P(x) B. (∀x)(∃y)P(x, y) ≡ (∃y)(∀x)P(x, y) C. (∀x)(P(x) → Q(x)) ≡ (∃x)(P(x) ∧ Q(x)) D. (∀x)(P(x) ∧ Q(x)) ≡ (∀x)(P(x) ∨ Q(x))
Exercise 6| We introduce a language in which there are: - A constant me which represents the person who speaks, and a constant vegetables which represents the corresponding food; Two symbols of binary relations eat and likes: eat(p, a) represents the property "p eat a" and likes(p, a) the fact that "p likes a ". 1. Give the logical formulas that correspond to the following expressions: (a) I like everything I eat. (b) There are things that I do not like but that I eat anyway. (c) Those who do not like vegetables eat nothing. (d) If everyone agrees to eat something he does not like then I eat vegetables.
Negating Formulas with Nested Quantifiers De Morgan's laws allow to rewrite the negation of a disjunction or a conjunction in a logical equivalent formula where the negation appears in front of the atomic propositions and not in front of a compound proposition: -(a A b) = ¬a V ¬6 ¬(a v b) = ¬a ^ ¬b
Express the statement using predicates, quantifiers and conditional connectives.“In every online class few students have connectivity issue and they do not join the class.”
Let M(x, y) be the statement "x is a role model for y," where the domain for both x and y consists of all people in the world. Use quantifiers to express "Someone is a role model for all people."* O 3xayM(x,y) O vx3yM(x,y) O None of the mentioned O 3XVYM(x,y) O VXVYM(xy)
. 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.
1
1. Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers. a) x Vу (ху -у) b) Vx Vy(((x 0)) c) 3x 3y ((x2 > y) ^(x
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