1. Rewrite the statements so that negations appear only within predicates (so that no negationis outside a quantifier or an expression involving logical connectives) (1)-Vx (D(x) (A(x) V M(x)))2. Prove that the following expressions are logically equivalent by applying the laws of logic (1(pq) (p V q) and T3. Use a truth table to show whether the logical expression is a tautology, contradiction or neither-(p→q) → p

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Answered: 1. Rewrite the statements so that…

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.
Which of the following is a logical equivalence in first-order logic? A. ¬(∀x)P(x) ≡ (∃x)¬P(x) B. (∀x)(∃y)P(x, y) ≡ (∃y)(∀x)P(x, y) C. (∀x)(P(x) → Q(x)) ≡ (∃x)(P(x) ∧ Q(x)) D. (∀x)(P(x) ∧ Q(x)) ≡ (∀x)(P(x) ∨ Q(x))
I don't like Superman. I don't like Spiderman. -8- 7. We know that since p→q=pVq, that any expression we could write with "implies" can instead be written with only "not" and "or." Write an expression equivalent to p^ q that uses only the logical operations V and. Prove it is equivalent with a truth table.
a) Use the rules of inference and laws of logic to prove the validity of the following argument. Provide the steps and reasons. [(-rvq)^(-s)^(-r→s)]= q
Consider the following predicate, where the domain of x and y is the set of all integers: Q(x, y) : x - y = 3 Determine the truth values of each of the following expressions. ¡¡ x\yQ(x, y) Q(4,1) Q(7,4) VxyQ(x,y) Q(4,7) 1. True 2. False
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
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.
Prove that -(p → q) + -q and T are logically equivalent by applying the laws of propositional logic.
EXERCISE 1.11.1: Valid and invalid arguments expressed in logical notation. Indicate whether the argument is valid or invalid. For valid arguments, prove that the argument is valid using a truth table. For invalid arguments, give truth values for the variables showing that the argument is not valid. (h) (1) q→p -q Ap -(p→q) 9 p -q -(p→q) Р q→P q→P P :-(p→q)
Use truth tables to determine if the following statement is tautology: [(M-) v (U→S)] (M→S) Use the editor to format your answer maining

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