Translate each of these statements into logical expressions using predicates, quantifiers, and logicalconnectives.a) Something is not in the correct place.b) All tools are in the correct place and are in excellentcondition.e) Everything is in the correct place and in excellentcondition.d) Nothing is in the correct place and is in excellent condition.e) One of your tools is not in the correct place, but it isin excellent conditionWAD

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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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Translate each of these mathematical statements into logical expressions. Assumethe domain is all integers.(a) The product of two integers is always non-positive if one of them is negative butnot both.(b) The square of an integer is not always greater than itself.
Deduce using known properties that the statement:[(p ∧ ∼q) v (p ∧ r)] ⇒ (q ∧ r) is the negation of: ∼ (p ⇒ q)
c and d part solution
part D E
Exercise 7. Let x and y be real numbers. (a) Let A be the sentence “If x + y > 0, then x > 0 or y > 0.” Use Theorem 2.10 and one of De Morgan’s laws to show that ¬A is logically equivalent to “x+y > 0 and x ≤ 0 and y ≤ 0.” Be careful not to skip any steps. (Hint: To save writing, feel free to use the abbreviation “≡” for the phrase “is logically equivalent to.” It may help you to review Example 2.3.) (b) Is the sentence A in part (a) true, or is ¬A true? Explain why. (c) Let B be the sentence “If x + y > 2, then x > 2 or y > 2.” Is B true, or is ¬B true, or is it impossible to say without further information about the specific values of x and y? (Hint: Can you find specific values for x and y for which B is true? If so, give an example of such values. Can you find other specific values for x and y for which ¬B is true? If so, give an example of such values.)
Consider the two following logical expressions: (1) (p → q) → r (2) p → (q → r) Let the first expression be X and the second expression be Y. With proof, determine which of the following (if any) is a tautology? (a) X → Y (b) Y → X
* A propositional variable p is a formula. (It is assumed that there are infinitary many such variables p, q, r, p1, p2, ...) * If A is a formula, then (~ A) is also a formula. * If A, B are formulas, then (A A B), (A v B), (A → B), (A = B) are formulas, respectively. *if A is a formula, then •A and OA are formulas, respectively. * We use - A, AB to mean ¬A, A → B, respectively since we use the text book by Girle [1] (See below). - Exercices. Give examples of formulas and explain why they satisfy this definition.
1) Express the statements below using quantifiers. 2) Form the negation of the statement in logical form. 3) Express the negation in simple English "Everyone likes Pixars movies" Show your work on paper, digitize it, and upload it here.
Q7. Let z and y be propositional variables, and let P₁: zvy Pr:x A-y Ps: yr C:y Answer the following three questions, in order: • Is the argument (P₁ P₂^ P3) → C valid? • Is the set {P₁, P2, P3} consistent? • Are P₂ and-P3 logically equivalent? A. Yes, no, yes. B. No, yes, yes. C. No, yes, no. D. Yes, no, no. E. Yes, yes, yes. F. No, no, yes. G. none of the above.
CompSci- Discrete Maths (propositional logic)image attached
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.
Classify each entry in the list below as: an English noun (NOUN), a mathematical expression (EXP), or a sentence (SEN). In any sentence, circle the verb. Classify the truth value of any entry that’s a sentence: TRUE (T), FALSE (F), or SOMETIMES TRUE/SOMETIMES FALSE (ST/SF).

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Translate each of these statements into logical expressions using predicates, quantifiers, and connectives. a) Something is not in the correct place. b) All tools are in the correct place and are in excellent condition. e) Everything is in the correct place and in excellent condition ΝΑΙ