B. Let Plx,y) þe the statement " student x has takenwhere the domainICS and for y consistsog Hese quantifuotionfor x consits ofall computer scenà studentsof* all mathumahes courses. Express eachEnglish sentenes.¥x ¥y P(x.y)Vy Hx P(x,g)¥x 3y P(X.y)

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Answered: B. Let Plx,y) be the statement student…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Q7: Translate the following statement into English, where R(x) is "x is a rabbit" and H (x) is "x hops" and the domain consists of all animals. • 3x(R(x) → H (x)) Q8: Translate in two ways the following statement into logical expressions using predicates, quantifiers, and logical connectives. First, let the domain consist of the students in your class and second, let it consist of all people. Everyone in your class has a cellular phone. Q9: (* Let P (x, y) be the statement "Student x has taken class y," where the domain for x consists of all students in your class and for y consists of all computer science courses at your school. Express the following quantification in English. 3XVYP (x, y)
Let T(x,y) = "x will take y", S(x) = "x is a CS student", H(y) = "y is a hard course" and P(y) = "y is an elective course" Assume the domain of x is all students and the domain of y is all courses. Select the negation of "Some CS students will not take all elective courses" O 1.All CS students will take some elective courses. O 2. All students will not take all elective courses. O 3. Some CS students will not take some elective courses. O 4. Some CS students will take all elective courses.
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.
QUESTION 3 Determine if the following logical expression is a tautology or contradiction. (p^¬q) v (qv-p) O Neither tautology nor contradiction O Tautology Contradiction Both tautology and contradition QUESTION 4 Match the set operation with its definition. AnB a. {xlx EA and x = B} AUB b. {xlx EA or x = B} c. {xlx EU and x # A} d. {xlx EA and x & B} A A-B
2. Which is the main connective of the following sentence: -(F G)→ H A. - B.. C. → D. () 3. Which is the main connective of the following sentence: {[-(A-B) v C]~D} v E A. - B. → C. V D. →
33. Rewrite each of these statements so that negations ap- pear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives). x(x, y) a) xy(x, y) c)x(P(x, y) v Q(x, y)) d) (x³y-P(x, y) e)x(yz(x, y, z) z(x, y, z) b) x(x, y))
Which of the following is/are tautology? O a. avb→ b^c O b. a^ b→ bvc O c. avb→ (b→ c) O d. Both (a) & (b) O e. Both (b) & (c)
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)
Exercise 5.6.1: Which expre zy 5.6. Predicates and quantif FHW4-Logic Answered: First, launch Net zy 7.4.Streams using Strings x Fall 2019 STUDENT Survey x + X x X X IST 230: Language, Logic, and Discrete Mathematics home 5.6: Predicates and quantifiers = zyBooks oliver oladeji Help/FAQ zyBooks catalog Exercise 5.6.3: Translating mathematical statements in English into logical expressions. About Consider the following statements in English. Write a logical expression with the same meaning. The domain is the set of all real numbers (a) There is a number whose cube is equal to 2. (b) The square of every number is at least 0. (c) There is a number that is equal to its square (d) Every number is less than or equal to its square Feedback? Evercise 56 4: Truuth value for auantified statements for a given set of nredicates About
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.
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Let P(a, b) and Q(a, b) be the open sentences defined by P(a, b) : a = b andQ(a, b) : a^2 − b^2 = 0, respectively, where the variables a and b can take any value in Z. Determine the truth value of the open sentence Q(a, b) ⇒ P(a, b) for each (a, b) ∈ {(2, −2),(5, 7),(3, 3)}. Explain your answers. (Z is the set of intergers)

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B. Let Plx,y) be the statement student x has taken where the domain all computer screnà students of ICS and for y umšists g Hese quantifustion for x consits of * all mathumahus courses. Express cach English sentences. ¥x¥y P(xy) Vy H x P(x, g) ¥x 3y P(x.y)