For each numbered line that is not a premise in each of the formal proofs that follow state the rule of inference/replacement that justifies it. 1. (T · (UƆ V))4, 6 Addition( ( (W.X) כ U) כ T) .23. ((T · V) Ɔ ~ (W v X))3, Transposition.: (W = X)4. ((T · U) ɔ (W ·X))5. (T· V) ɔ ( ~ W. ~ X))6. ((T · U) ɔ (W·X))·((T. V) ɔ (~ W. ~ X))7. (T · U v (T. V))6, 7, Constructive Dilemma8, Material Equivalence8. ((W. X) v (~W v ~ X)9. (W = X)1, DistributionPromptsSubmitted Answers2, TautologyHow did we arrive with line number 4?2, Exportation3, De Morgan's TheoremHow did we arrive with line number 5?Choose a match2, SimplificationHow did we arrive with line number 6?Choose a match8, 5, Hypothetical SyllogismHow did we arrive with line number 7?Choose a match1, AbsorptionHow did we arrive with line number 8?Choose a match4, 5, Constructive DilemmaHow did we arrive with line number 9?Choose a match

Answered: For each numbered line that is not a…

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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Which of the following is TRUE about direct proof? O a. The negation of both the conclusion and the hypothesis b. Straightforward deductions O. An induction step and a conclusion o d. The negation of the conclusion
Question 27 Using a full-length truth table, determine the logical status of the following argument form: K (MVH) / MH/MOK // KOH Invalid; fails in 4th line O Invalid; fails in 3rd line Invalid; fails in 2nd line Invalid; fails in 1st line O Valid Question 28 From left to right, what are the truth values under the main connectives on the fourth line of the truth table for Question 27? O F.T.T.T OT.T.F.T OF.T.F.T OT.T.T.F. OT.T.F.F.
1. Prove the following using a truth table. (O is a symbol for XOR.) p@q = (p V q)^ ¬(p^q)
a)find a proposition using only p, q, and ~ (negation) and V (or) b) find a propostion with three variables p, q, and r that is false when at least one of the prepositons is true and is true otherwise
Some lions are ferocious. Lambert is a lion. Therefore Lambert is ferocious. The above argument is Select one: O i. Valid and unsound O ii. Invalid and sound O iii. None of these O iv. Valid and sound O v. Invalid and unsound sentence P is truth functionally true if and only if Et one: {P} has a closed truth
For each proof, you must include (i.e., write) the premises in that proof. Proofs must have premises. Conditional Proof (CP), Indirect Proof (IP) and Assumed Premises (AP) are not allowed to be used. Only the 18 rules of inference can be used. Points will be lost if you use any of the inference rules Resolution, Contradiction, Transposition, Idempotence and Identity. Only answer questions 7, 9 and 11.
In logic what is the difference between propositional forms that are necessarily equivalent and propositional forms which are equivalent? In chapter 1.1 of book “A Transition to Advanced Mathematics” by Douglas Smith, he states two propositional forms are equivalent if they have the same truth table. The book doesn’t mention anything about “necessary equivalence” until chapter 1.1, exercise 9: “Suppose P, Q, S, and R are propositional forms, P is equivalent to Q, and S is equivalent to R. For each pair of forms, determine whether they are necessarily equivalent. If they are equivalent explain why.”
QUESTION 13 Make a truth table to determine whether or not the logical argurment below is valid. Show the truth table and state your concluston de b
The following problem is that of Discrete Mathematics. Consider the following implication, where n stands for an unknown integer.“If n is divisible by 10, then n is divisible by 5.” a. Write the equivalent “or” form of this implication as an English sentence. b. Write the logical negation of this implication as an English sentence. (Do not use “It isnot the case that…”)
1. Using a truth table, prove De Morgan's laws as follows. ¬(pVq) = -p A ¬q & ¬(p^q) = -pV¬q

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