Let P(x, y) be the statement "Student x has taken class y,"where the universe of discourse for x consists of allstudents in your class ad for y consists of all engineeringcourses at your school. Express vyax P(x, y)There is an engineering course that everyAstudent in your class has taken.There is a student in your class who has takenevery engineering course.Every student in your class has taken everyengineering course.Every engineering course has been taken by atDleast one student in your class.

P(x, y) means "student x has taken class y".

Answered: Let P(x, y) be the statement "Student x…

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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please solve (b)
Determine which of the following logical notations is a tautology, contradiction, or contingency.
Let P(x, y, z) denote the statement x³ - y³ = z. Let the universe of discourse for x, y, and z be Z‡. 3 Consider the following statements: (1) Vx Vzy P(x, y, z). (2) Vz 3x3y P(x, y, z). Select one of the following choices: (a) (1) is True and (2) is False. (c) (1) and (2) are True. (b) (1) is False and (2) is True. (d) (1) and (2) are False.
CREATE A TRUTH TABLE
10. Construct the truth table for [(pq) v (p → r)] → (-q ^p).
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
Choose O if the statement is ALWAYS true. Otherwise, choose X. No need for justifications. ◆ (a.) The logic expressions (p → (q→r)) and ((p ^ q) →r) are logically equivalent. ◆ (b.) Suppose the proposition p V q is true, but we do not know which of p or q is true. If p→r and q→ r, then regardless of which of p or q is true, then we can infer proposition r to be true. ♦ (c.) Let A be a finite set of n elements. Then the number of subsets of A is n². (d.) If the symmetric difference of two sets is empty, then those two sets are equal. + (e.) Consider the divides relation x Ryxy. If R is defined over the set of all integers Z, then R is a partial-order relation. ♦ (f.) Let X and Y be finite sets. If there exists a function f : X→ Y that is one-to-one, then X ≤ Y powerset P(S) is also countable. ◆ (g.) If a set S is countable, then its (h.) The infinite union of finite sets is countable. → (i.) Let F(x)= automorphism on (R+, .) - x². F is an ♦ (j.) The set of non-zero real numbers with…
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.
Prove the validity of the argument using two-column proofs (Statement - Reason).
2. Using logical equivalence, prove that (p^q)⇒(q⇒p) is a tautology. In other words, show that (pa)(a⇒p)=T You have to give clear reasons for each step!
6. Match each logical statement in the left hand column with an equivalent logical statement in the right hand column. Logical Statement (i) ~ WA~y Logical Statement (v) w v ~y (ii) wA~y (vi) ~ (~w→ y) (iii) w v y (vii) ~ (~w v y) (viii) ~ w → y (iv) ~ (~WAy)
Do these three short problems

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