5. (i) Write each of the two arguments below in 'Boolean goggles' form, using the letters A, B,C etc., in the same order that they first appear in each argument.(ii) Say whether or not each argument is a logical consequence, and whether or not it is atautological (TT) consequence.(a)Boolean goggles:(b)(BackOf(b, e) A Cube(b))BackOf(b, e)-Cube(b)Logical consequence?TT con?BackOf(b, e) v Cube(b)b=eרDodec(b)Logical con?Boolean goggles:TT con?(iii) Show that one of the arguments above is not TT con by filling in one row of a truth table)

In the provided logic question, the task involves translating logical arguments into a simplified…

Answered: 5. (i) Write each of the two arguments…

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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Similar questions

- 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).
If LIx) represent the propositional logic then what is the meaning of given below statement "VxL(x) and "a xL(x)"?Explain briefly.
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
Using the following translation key, translate each of the sentences of English, (i)-(vi), into PL.P: There is alien lifeQ: Humans are the only intelligent lifeformsR: Dogs are intelligentS: God existsT: Humans evolved(i) Either God exists and humans are the only intelligent lifeforms, or God doesn’t exist and there is alien life(ii) There is alien life only if God doesn’t exist(iii) Humans are the only intelligent lifeforms unless either there is alien life or dogs are intelligent(iv) God doesn’t exist just in case both humans evolved and they are the only intelligent lifeforms(v) If God exists and humans evolved, then if God exists then humans are not the only intelligent lifeforms
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.
3. Let us consider the propositional language where: A = "Peter does his homework" B = "Burt does his homework" C = "Andy does his homework" D = "Dexter comes to the party" Write the statement for the following symbols. (d) C → (~D → ~A) (e) (~D → C) A (D → ~B) (f) A A~BAC → ~D) a ( A a B → (D → C)

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