**Logical Expressions of Quiz Show Participation**Let \( Q(x, y) \) be the statement "Student \( x \) has been a contestant on quiz show \( y \)." Express each sentence in terms of \( Q(x, y) \), quantifiers, and logical connectives, where the domain for \( x \) consists of all students at your school and for \( y \) consists of all quiz shows on television.**(a)** There is a student at your school who has been a contestant on a television quiz show.**(b)** No student at your school has ever been a contestant on a television quiz show.**(c)** There is a student at your school who has been a contestant on *Jeopardy!* and on *Wheel of Fortune*.**(d)** Every television quiz show has had a student from your school as a contestant.**(e)** At least two students from your school have been contestants on *Jeopardy!*

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Answered: 8. Let Q(x, y) be the statement…

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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Suppose that A ==> B is true. Which is then automatically true, the converse or the contrapositive?
DO NOT COPY FROM OTHER WEBSITES Correct and detailed answer will be Upvoted else downvoted. Thank you!
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))
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
30. Rewrite each of these statements so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives). (a)¬у³x²(x, y) (b) -VryP(x, y) (c) y(Q(y) AV-R(x, y)) (d)¬Jy(R(x, y) V VxS(x, y)) (e)y (VxzT(x, y, z) VrVzU (x, y, z)) 7
. If the domain consists of all animals, express the following statements in terms of quantifiers and logical connectives, where B ( x ) = x is a bear, G ( x ) = x raids garbage cans, H ( x ) = x loves honey, and T ( x ) = lives in tents. A bear lives in a tent. Bears love honey. Only bears raid garbage cans. No bear lives in a tent. Some bears do not love honey.
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.
Apply De Morgan's law to the following expression to obtain an equivalent expression in which each negation sign applies directly to a predicate. (P(x) ^ (Q(x) v R(x))) O 3x (-P(x) v (¬Q(x) ^ ¬R(x))) -3x P(x) or 3x ¬(P(x) ^ Q(x)) O 3x (P(x) v (Q(x) ^ ¬R(x))) O None are equivalent.
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.
Using relational predicates ( e.g. F(s,m) for, say, s can fool m), translate the following sentences into predicate logic. You can use English words for the quantification symbols (such as For All x instead of v x) if necessary Also give the negatives of each sentence in English. a) Everybody can fool somebody b) There is no-one who can fool everyone. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
Any time you see A, B, or C in any of the quiz questions, those statement letters are true. Any time you see X, Y, or Z in any of the quiz questions, those statement letters are false. Not all letters, (A, B, C, X, Y, Z), will be in all statements. (-Av-C)v (X A) True False
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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