1. Justify each statement which is not a premise using the rules ofinference to complete the formal proof of validity of the argument.1. f→→g2.¬f → (h→→g)3. (iv-h)→→g4. ¬i5. -iv-h6.7.8. h→-g9.hgf11::-h

We write the rules of inference in the respective row that is used in the proof.

Answered: 1. Justify each statement which is not…

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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Translate the following argument into symbols and prove its validity using rules of inference. No contractors are dependable. Some contractors are engineers. Therefore, some engineers are not dependable. Hint: Use the following symbols. C(x):xis a contractor. D(x):x is dependable. E(x):x is an engineer.
Kindly answer both the questions asap
Show work please
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.
Construct a direct proof of validity for the given arguments below using rules of inference and equivalence. 1. B ∧ C B →∼ (C ∧ D) E → D ∴∼ E (use direct formal proof of validity)
4. Let P be "It is humid" and let Q be "sum of 9 and 11 is 21". Give a simple verbal sentence which describes each of the following statements: (a) ¬Q, (b) P V Q, (c) (¬P) ^ Q, (d) (¬P) V (–¬Q).
Which statement is logically equivalent to (P→Q) O ¬(Q→P) OPAQ OPV¬Q O¬¬Q
Use an indirect proof to show that each conclusion follows logically from the premises: P V Q R → -P 1. Premises: -(Q V S) Conclusion: ... -R Show that the hypothesis "it is not sunny this afternoon and it is colder than yesterday", "we will go swimming only if it is sunny", "if we do not go swimming, then we will take a canoe trip", and "if we take a canoe trip then we will be home by sunset". Lead to the conclusion: "we will be home by sunset." 2.
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-
1. Is (P + Q) → (P= Q) a tautology? Explain.
a 46 | ooredoo 1. Use the truth table to check the following are logical equivalence or not? a. pqpV q b. pAq-(p¬q) c. (p→q) A (p → r) =p→ (q Ar) d. (p r)V (q→r) = (p^q) →r e. p+q= (p→ q) ^ (q → p)
Only need help with 4c. I had put addition but got it wrong.

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1. Justify each statement which is not a premise using the rules of inference to complete the formal proof of validity of the argument. 1. f→-g 2. 3. 4. ¬i 5. -iv-h 6. g 7. -f 8. h→-g 9. -h ¬f → (h→→g) (iv-h)→g 11::-h