Prove the validity of the following sequents, assuming the binding priority of the connectives covered in1.class:+ p- q.r→s E pV r→qVs+ (p V (q → p)) ^ qF p+ p- (qV r), q → s, 1→SF p→s

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Answered: Prove the validity of the following…

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 T(s) denote s is a technologies major, C(s) denote s is a computer science student and E(s) denote s is an engineering student. If the domain set of all students in CityU rewrite the following statements by using quantifiers, variables, and predicates T(s), C(s), and E(s).(i) Every computer science student is an engineering student.(ii) Some computer science students are also technology majors.
Explain what are the differences, if any, between a structure of L₂ (the language of predicate logic) and a structure of L (the language of predicate logic with identity).
Let A, BCU. Complete the following proof of the statement given below. (AUB) n(AUB) CA, where Bº = U\B. Proof: By distributivity of disjunction with respect to conjunction, and x € (AUB) n(AU Bº) ⇒ (x € An (AUB²)) Since An A = Now, since BnB = x € ((ANA) U (An Bº)). Since An BCA, Thus, x = ( Since An BC CA and AUA = A, Then since (An B) u0= x € (AU (An Bº)) U ((BNA) U U (An Bº)) U ((B^ A) U (B^ Bº)) . AU (ANB) C TEAU ( ((BNA) U (Bn Bº)). x EAUA = (Bn(AUB)), (AUB) n (AUB) ≤ A
(11) Let P be the statement: "For all a, b = Z, if a + b is divisible by 10, then a is divisible by 10 and b is divisible by 10." (a) Express P using logic symbols, denoting the set of all multiples of ten by T. (b) Find ¬P, in both logic symbols and in english. (c) Find the contrapositive of P. (d) One of P or P is true. Determine which one, and justify your answer.
3 B and D please
Given the domains m e MOVIES and ce CHARACTERS and the following predicates: • sW(m): m is a Star Wars movie. A(c, m): c is a character who appears in the movie m • D(c): c is a Droid. • L(m): I liked m. • Q(c, q): c says q (e is quoted as saying q.) • jarjar is the character Jar Jar Binks • bad is the quote: "I've got a bad feeling about this!"
. 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.
For the following questions use these symbols to represent the connectives and, or, and not: And: && Or: || Not: ! Which of the following is the negation of p || q? i.e. !(p || q) is equivalent to ? Select one: a. !p && !q O b. !p && q O c. !p || !q O d. !p || q
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.
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).
Exercise 1. Express the following statements symbolically using multiple quantifiers. De- fine your domains and two-variable predicates. Then negate the statements. (a) Every rational number when multiplied by some integer is an integer. Domain(s): • Predicate: • Statement: • Negation: ● Englsih translation of negation: . Which is true? The original statement or its negation? Justify your answer.

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Prove the validity of the following sequents, assuming the binding priority of the connectives covered in -lass: + p- q. r→ sF pV r→qV s