Write negation for each following statements All dinosaurs are extinctNo irrational numbers are integersSome exercises have answersAll COBOL programs have at least 20 linesThe sum of any two even integers is evenThe square of any even integer is even

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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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2 Translating English Sentences into Formulas Consider the following two predicates: S(x) : x is a student in CSE015; M(x) : x plays a musical instrument. Let the domain be the set of all people. Using the above predicates, translate the following sentences into formulas using the appropriate quantifiers and operators. a) Not every student in CSE015 plays a musical instrument. b) A person is either a student in CSE015 or plays a musical instrument, but not both. c) There exists at least one student in CSE015 who does not play a musical instrument.
Write the negation of each of the following statements. a. Some Web sites feature audio. b. Every Web site has both audio and video. c. Every Web site has either audio or video. d. Some Web sites have neither audio nor video. e. Every Web site either has text or else has both audio and video.
Rewrite the following statements and their negations using quantifiers and symbols. Then, argue whether the statement or its negation is true by proving the statement or by finding a counterexample. (a) There is a rational number which is greater than its square root. i. Original statement: ii. Negation: iii. Which is true and why? (b) Each integer has the property that its square is less than or equal to its cube. i. Original statement: ii. Negation: iii. Which is true and why? (c) Every element in the set {0, 1,2} is greater than or equal to half of its square. i. Original statement: ii. Negation: iii. Which is true and why?
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)
Express the following statements in predicate logic: Some human is not mortal. For every x and every y there exists a z which is the sum of x and y. There is no prime number between 23 and 29.
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.
Express the following statement using mathematical and logical operators, predicates and quantifiers, where the domain is the set of integers (i.e. translate into symbolic form). Then prove the statement. "If the difference of squares of two integers is even then they have the same parity" (Note: two integers have the same parity if both are even or both are odd)
Complete the table to express the values of each of these Boolean functions.
Rewrite the following statement in the form "v All Java programs have at least 5 lines. X, if then 11
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Proficiency #6. (a) Write the negation of the following statement without using ¬. (3x € Z)(Vy E Z)( € Z)(x+y = 5k + 1) (b) Complete the following in predicate logic form: "Given integers a and b and a natural number n, the integer a is congruent to b modulo n if ..."

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All dinosaurs are extinct No irrational numbers are integers Some exercises have answers All COBOL programs have at least 20 lines The sum of any two even integers is even The square of any even integer is even