1. Using the abbreviations specified below, symbolize the following English sentences in the language oftruth-functional logic.A: Killing zombies is morally permissible.B: Zombies are persons.C: Zombies have a right to unlife.can asins monilly poenitabl, onis if zombiAMAMlingombeha th Vit unlifeb.(A →~B) → Cue'· pe ons io naje a right toThe amis a tal pro mas for yif not use areiɔt na zona resa e2. Assuming that the propositional constants are used to abbreviate statements as given in the previousproblem, translate (a) and (b) below into smooth, unambiguous, idiomatic English.a. B → (~C → A)Page Break2107 arun'assa dies vs ve long ito a life k lins zon sies to beFACE

Given: A: Killing zombies is morally permissible. B: Zombies are persons. C:…

Answered: 1. Using the abbreviations specified…

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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Using rules of inference, laws of logical equivalences, and other definitionstaught in class, show that the premises conclude with “It is not true that“If I turn in my homework, then I will go to sleep early”” Be sure todefine all propositional variables for full credit. Remember, it is possiblethat you will use all premises, but it is also possible that some are notneeded. a.) Today is Friday and Papa Johns is on fire.b.) I will win a chess match if today is a Friday or I do not watch amovie.c.) I sleep early only if I do not win a chess match.d.) I will get to class on time and turn in my homework if I do not sleepearly.e.) Papa Johns is not on fire if and only if I do not turn in my homework.f.) Domino’s is not on fire today.
1. Given premises: (1) I would read a book or go to gym on Sunday (2) If Peter does not go to the gym Sunday, I would not go to the gym on Sunday (3) If Peter would go the the gym on Sunday, he would take a rest on Saturday (4) Peter does not take a rest on Saturday. Prove the conclusion: I read a book on Sunday. You should first express the premises and the conclusion using propositional logical expressions. Use rules of inference and follow the format for formal proofs discussed in class.
Consider the domain of people and the following argument: Hypothesis: If a person is a mathematician, then he/she is a programmer. If a person is a programmer, then he/she is prone to headaches. Conclusion: Therefore, if a person is a mathematician, then he/she is prone to headaches. a. Assign letters to the basic propositions and write each hypothesis and the conclusion as an implication. ● Hint: Use the syntax P(X) : “X > 0” or P(X) : “subject and predicate" to represent your statements. b. Prove the correctness of you answer to item a. by using the logical equivalencies and/or rules of inferences tables from your text which are also available below.
7. Using your general knowledge of the world, please state whether each line of the argument (copied from above) is a true statement or a false statement. (Note: Today is Saturday January 22, 2022) If today is not Christmas then Christmas will never happen. Today is not Christmas. - Christmas will never happen. (Tor F) (Tor F) (T or F) B. What do your answers say about the argument?
7. Describe the following combined propositions as English sentences if s = heavy snow, C = flight canceled, and d=there are delays a. s→C b. sAc (s V c) • (d V c) e. sA (d V c) С. d d. s- 8. Convert the following expressions into DNF format (where ! is NOT) a. (x+y!z)(!x+y+!z) b. (ху)!(х+y) 9. Are the following expressions satisfiable? a. (x+y)(!x+!z)(!y+z)(x+!z+!y) b. (x+y)(!x+!z)(!y+z)(x+!z+!y)(!x+y+!z) 10. Draw circuit for the following expression !xy(!x+y)(x+y+!z)
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.
For each logical argument, select all the truth assignments for the propositional variables that show the logical argument is invalid. 1) 2) r S T T r T F T F p+ -q rv ¬S FT F T :- F F F F
Describe the following combined propositions as English sentences if s = heavy snow, c = flight canceled, and d=there are delays а. b. sAc c. d→ (s V c) → (d V c) e. sA (d V c) d. s-

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