5.Use the laws of propositional logic to prove that the following compoundpropositions are tautologies.а. ((р - 9) лр) — qb. ((p → q) ^ (¬p → r)) → (¬q → r) Idempotent lawsp V p = pd = dy d(p ^ q) Ar = p ^ (q ^r)Associative laws( φν) Vr=pV (q Vr .Commutative lawsp V q = q V pp^ q = q ^pDistributive lawsp V (q Ar) = (p V q) ^ (p V r) p^ (ą v r) = (p ^ q) v (p ^r)Identity lawspVF = pp^T = pDomination lawsp V T = Tp A F = FDouble negation lawsp קברComplement (ornegation) lawsp V ¬p = Tp^ ¬p = FDe Morgan's laws¬(p V q) = ¬p ^ ¬q¬(p ^ q) = ¬p V ¬qAbsorption lawspV (pΛq) pd = (b ^ d) v dConditional identitiesp → q = -p V qреда(р-д) л (q — р)

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Answered: 5. Use the laws of propositional logic…

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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09:22 Question 3 3. [30] Write each of these propositions by using propositional variables and the logical connectives. a) For you to win the contest it is necessary and sufficient that you have the only winning ticket. b) It is necessary to walk eight miles to get to the top of Long's Peak.
Let P, Q, and R be propositions. Consider the claim: (P → Q) v (R → Q) = (P ^ R) → Q. 4a) Use truth tables to prove or disprove the above claim. 4b) Using the Laws of Logic (e.g. Theorem 2.1.1) to prove or disprove the claim.
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
need help with 1-16
Using truth tables, or in any other way, prove that each of the following compound propositions is not a tautology. These implications are common logical fallacies (errors in reasoning) since the conclusion does not follow logically from the set of hypotheses. a. [(P⇒ Q) ^ Q] ⇒ P. b. [(PQ) ^ (~ P)] ⇒ (~ Q). For each one of the logical fallacies in part (iii) of this question give an example of a "real life" situation where such an error can occur.
Use propositional logic to prove that the argument is valid. 1. AAB'A [Bv (A' v C)] → C 2. (A V D) A (B'→ C) A (AC) → D
2. Use a truth table to justify the following logical equivalence: - (p → q) V r = (pV r) ^ (~ q V r)
8. Determine the truth value of the each of these statements if the domain consists of all integers: а. Уп(п + 1 > п) b. 3n(n = 1) с. Эn(2n 5n) d. Vn(3n<4n) e. 3n(n?: - 1)
Use the rules of inference and the laws of propositional logic to prove that each argument is valid. Number each line of your argument and label each line of your proof "Hypothesis" or with the name of the rule of inference used at that line. If a rule of inference is used, then include the numbers of the previous lines to which the rule is applied. 비 (c) (d) D EXERCISE 1.12.2: Proving arguments are valid using rules of inference. → P→ (q^r) -q -P (p^q) →r -r 9 :-P (pvq) →r p Ar pvq -pvr -q p→q r-u par q^u Feedback?
Only need help with 4c. I had put addition but got it wrong.

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5. Use the laws of propositional logic to prove that the following compound propositions are tautologies. а. ((р - q) лр) — q