QUESTION 10Consider the following statements:T(x, y): "x eats y".A(x): "x is wise".S(x): "x is hungry".F(y): "y is fat".H(y): "y is healthy".The domain of x is the set of all people and the domain of y is the set of all food.Select the symbolic of the following statement:"Mike is hungry and wise but do not eat all healty food"None of the proposed answers.Vy A (Mike) AS (Mike ) V [H (y) ^ ¬T(x,y)]3y A (Mike ) AS (Mike) ^[H (y) → ¬T(x,y)]Vy A (Mike) A S (Mike) V [H (y) → ¬T(x,y)]Vy A (Mike) AS (Mike) ^[H (y) → ¬T(x,y)]

Answered: Consider the following statements: T(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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Let M(x,y) be the predicate "person x has seen movie y," where the domain for x is the set of all people and the domain for y is the set of all movies. Express the following English sentence as a symbolic proposition: "There is a movie that has not been seen by any people." x-M(x,y) ⒸyVx-M(x, y) x-M(x,y) yx M(x,y) -
Let p and q represent the following statements. p: Interest rates are low. q: It is not time to buy a house. Write the following statement in symbolic form: "Interest rates are not low, and it is not time to buy a house." To enter your response, select the appropriate statement in each of the dropdown boxes, and select the appropriate operation in the middle. If only one statement is used, select "none" for the operation in the middle and the statement in the second dropdown box. Be sure to enter the statements in the same order as in the given sentence. A OV Onone (Select an answer ?
Translate the following sentence in terms of predicates, quantifiers, and logical connectives. Choose your own variables and predicate statement symbols as needed and define each of them clearly. Specify the domain
21. Let the following predicates be given. The domain is all computer science classes. I(r) = "x is interesting." U(x) = "x is useful." H(x, y) = “x is harder than y." M(x, y) = “x has more students than y." (a) Write the following statements in predicate logic. i. All interesting CS classes are useful. ii. There are some useful CS classes that are not interesting. iii. Every interesting CS class has more students than any non- interesting CS class. (b) Write the following predicate logic statement in everyday English. Don't just give a word-for-word translation; your sentence should make sense. (3)[I(x) A (Vy)(H(x,y)→ M(y, x))] (c) Formally negate the statement from part (b). Simplify your negation so that no quantifier lies within the scope of a negation. State which derivation rules you are using. (d) Give a translation of your negated statement in everyday English.
Let p and q represent the following simple statements. p: Steve annoys Gabby. q: Gabby annoys Steve. Write the symbolic statement q^p in words. Choose the correct sentence below. O A. Gabby does not annoy Steve or Steve annoys Gabby. O B. Gabby annoys Steve and Steve does not annoy Gabby. O C. Gabby does not annoy Steve and Steve annoys Gabby. OD. If Gabby annoys Steve, then Steve does not annoy Gabby.
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.
Let P(x) denote the statement "x is taking Math 111s". The domain of discourse is the set of all students. Write the following in words. 1. VxP(x) 2. Зх-Р(х) 3. ЭХР(x)
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A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refers to whether person x is an officer of the club. The predicate D(x) indicates whether person x has paid his or her club dues. The domain is the set of all members of the club. The names of the members and their truth values for each of the predicates is given in the following table. Indicate whether each expression is true or false. If a universal statement is not true, give a counterexample. If an existential statement is true, give an example. Name M(x) O(x) D(X) Hillary T F Bernie F F Donald F F Jeb F Carly F F Ex (M(x) A D(x)
2. Let P(x) be "x is a student in this class," Q(x) be “x knows how to write programs in Python," and R(x) be “x can get a good job," where the domain of x consists of all people. Write the following argument in argument form and use the rules of inference to show that the argument is valid. Tom is a student in this class. Tom knows how to write programs in Python. Everyone who knows how to write programs in Python can get a good job. Therefore, some student in this class can get a good job.
Let p: you see lightning and q: you hear thunder. Write each of the following statements in symbolic notation: a. If you see lightning, then you hear thunder. b. If you hear thunder, then you see lightning.. c. If you don't see lightning, then you don't hear thunder. d. If you don't hear thunder, then you don't see lightning.. If you see lightning, then you hear thunder. If you hear thunder, then you see lightning If you don't see lightning, then you don't hear thunder If you don't hear thunder, then you don't see lightning 114 114 #p-q =q-p

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