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.a. Killing zombies is morally permissible only if zombies neither are persons nor have a right to unlife.b. Killing zombies is morally permissible if and only if it is not the case both that zombies are persons andthat they have a right to unlife.C.Zombies are not persons; however, unless zombies have no right to unlife, killing zombies fails to bemorally permissible nonethelesº.

Given: The abbreviations A,B, and C for three statements.To find: The truth-functional logic for :a)…

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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4. Write each statement in symbolic form, and use truth tables to determine if they are logically equivalent: (define any variables you use) A: If you study hard and do all homework, then you will pass the class. B: If you study hard and did not pass the class, then you did not do all your homework.
Are the following expressions logically equivalent? (present a truthtable)~p ⋁ ~q ⋁ ~ r ; ~ (p ⋀ r ⋀ q)
A. The statement is not a tautology, since there is at least one combination of truth values for its components where the statement is false. B. The statement is a tautology, since it is true for all combinations of truth values of the components. C. The statement is not a tautology, since it is false for all combinations of truth values of the components. D. The statement is a tautology, since there is at least one combination of truth values for its components where the statement is true.
(a) Prove by using logical arguments (not by sketching Venn diagrams) that (AUB) = Aªn Bª.
2. Let p, q andr be the following statements: p: You run 10 laps daily. q: You are healthy. r: You take multi-vitamins. Translate the following into logical notation using p, q and r as logical connectives. a) You run 10 laps daily, you take multi-vitamins, and you are healthy. b) Either you are healthy or you do not run 10 laps daily, and you do not take multi-vitamins. c) If you do not run 10 laps daily or do not take multi-vitamins, then you will not be healthy.
3. Use a truth table to determine whether the following argument is valid or invalid. p → r ..p V q → r
Use truth table to establish the truth table of following 1)A conditional statement is not logically equivalent to its inverse
(a) Use a truth table to determine whether the following argument is valid. Be sure to indicate how you are reaching your conclusion. (Here t denotes a tautology) t → (~p V ~q) .. q → ~p (b) Use logical equivalences and standard forms to show that the following argument is valid. Fully justify each step of your claim. ~s → (r → ~p V ~q) .. S
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.”
Use the truth table test of validity to determine whether the following arguments are valid or invalid. To be invalid, the premises will be true, but the conclusion false. INSTRUCTIONS: 1. First, identify and define the type of Truth Functional Connective each symbol represents and type it in to the first table. 2. Then, create a Formal Method Test of validity table below each argument to determine whether the argument is valid or invalid. 3. Indicate whether the argument is valid or invalid. If the argument is invalid, highlight the area on the table that proves it. A row for each possible outcome [2"] → Use the pattern of half the rows to make half of the values in the column true → For the next column keep using the pattern of half Remember to Create: Type in the meaning of the symbol in the space provided. Truth Functional Symbol How to determine its truth value Connective it represents V .. SAMPLE ARGUMENT: 1. P• Q 2. .. Pv Q How many atomic propositions? = How many rows 2ª (+1…
Provide formal proofs or disproofs of the following arguments (using predicate logic and truth-functional statements with Rules of Inference in Math Logic) for the following problem: "If anyone puts Ketchup in the soup, then the soup will be spoiled. If it is spoiled, then someone will be furious with John. No one is furious with John. Therefore, John did not put Ketchup in the soup."
1. by using the laws of logic, Test the validity of the following argument: If I study then I will not fail. i did not fail Therefore i studied.

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