Translate the following argument into one of our formal languages (either zeroth-order or first-order), and then either give a proof of the conclusion from the premisses or show that the argument is not valid by using a truth table or a small world. After completing the translation and testing the validity of the argument, reflect on what it shows.   Every principle in ethics has some counter-example. If every principle in ethics has some counter-example, then Particularism is true.   Ethics is worth studying only if Particularism is not true.     Ethics is not worth studying.

Q: Evaluate the validity of the real life arguments using truth table.   If it is raining, then the…

A: Let P be the event of raining , Q be the event of muddy and R be the event of stuck If it is raining…

Q: Use truth tables to determine whether the argument is valid or invalid. The main course will be…

A: The main course will be Beef or fish  therefore , B∨F where B denotes beef and F denotes Fish  The…

Q: Show by means of a truth table that the sentence P ∧ (Q ∨ R) is not logically equivalent to the…

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Q: In each  represent the common form of each argument using letters to stand for component sentences,…

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Q: Show using truth-tables that the following formula is a tautology in propositional logic: (P→ Q) +…

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Q: 2. In this exercise we will explore the process of using a truth table to show that an argument is…

A: The 'or' symbol is denoted by. If one uses or between two statements , then this statement holds…

Q: What is the validity of the argument? "Some MMW students passed the exam. Sheila is a MMW student.…

A: Arguments: stament and conclusions

Q: What is the argument form for the following argument? If we assume the premises are true, is the…

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Q: Provide symbolic logical proofs (with truth tables or explained logical steps) of the following…

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Q: Use truth table to determine the validity of the following argument: P∧q ~(q ∧ r) Therefore, ~r…

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Q: Address the problems below about small worlds, models, and validity. a) What does it mean for an…

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: Use a truth table to determine whether or not the argument given by the following symbolic form is…

A: Given:        P→ ~ q,q∴ ~ p We have to determine whetherthe argument valid or invalid.

Q: i. If manufacturers raise the prices of their products or manufacturers do not raise the prices of…

A: We have "If manufacturers raise the prices of their products or manufacturers do not raise the…

Q: (P2⇒ (P3 V P4)) and ((P₂A-P4) ⇒ P3)

A: Given that the logical formulas P2⇒P3∨P4  and  P2∧¬P4⇒P3    .

Q: 7. Consider the following deductive argument: All vegetables are gross. Broccoli is a vegetable.…

A: The given statement is, Premise: All vegetables are gross. Premise: Broccoli is a vegetable.…

Q: Write the primitive statements of the following arguments and show them in symbolic form. Then…

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Q: Use rules of logic/ inference to prove the following argument. List each rule and proposition used…

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Q: Translate each English sentence into a logical expression using the propositional vari- ables…

A: Here, e: The student has permission to enroll from the instructor p: The student has completed the…

Q: Question: Use a truth table to determine whether the following argument is valid or invalid: 1.…

A: To determine the validity of this argument, we can use a truth table. We need to include columns for…

Q: Complete the logical proof for the following argument. p (qA r) Step Proposition Justification 1…

A: Given that the logical proof for the argument is p→q∧r¬q¬p

Q: "If all people obey the law, then no jails are needed. Some jails are needed.  __________________…

A: Let the prepositions are : all people obey the law : some jails are neededStatementsSymbolIf all…

Q: In order to prove an propositional argument invalid it is only necessary to find a propositional…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: 9. He is dumb or lazy. (D, L) He is dumb. Therefore, he is not lazy.

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Q: Given the following logical statements: p: All animals hop. q: Some senators are republicans. (1)…

A: Given p- All animals hopq- Some senators are republicans~q in words : Some senators are not…

Q: Construct a truth table to prove the following statement: (p→q)⇔(∼p∨q) Based on your truth table,…

A: We need to construct a truth table for ,  p → q ⇔ ~p ∨ q We know that ,  truth value of 'or' (∨) is…

Q: 6.) Construct and complete the truth table for the following formula: (~P→Q) V (R & ~Q)

A: We have to consider three propositions, P, Q, & R. In R&~Q we have to treat '&' as…

Q: Consider the following argument 1.All Hitchcock movies are suspenseful. 2.“Psycho” is a Hitchcock…

A: Let us consider ; p = It is a Hitchcock movie. q = It is suspensful r = It is  "Psycho"

Q: Use modus ponens or modus tollens to fill in the blanks in the arguments so as to produce valid…

A: Using modus tollens, we can derive a valid conclusion from the argument: "If logic is easy, then I…

Q: Define the necessary symbols, rewrite the argument in symbolic form, then use a truth table to…

A: Here, p: They are Pigs, q: They are Frogs, and r: They are green. Now, coming to the given…

Q: Determine if the following argument is valid or invalid. If it is valid, then translate it to logic…

A: The following arguments can be translated into logic as follows:1. All fleegles are snurds or…

Q: (a) Use DeMorgan’s Laws to write the negation of the following statement. Bob lied or I’m the Queen…

A: Solution: (a) (Bob lied or I'm the Queen of England)'      = (Bob lied)' and (I'm the Queen of…

Q: Consider the argument below: "If you complete your computer training, then you can be eligible to…

A: If you complete your computer training, then you can be eligible to work in the computer lab. You…

Q: If the truth table for a certain compound statement has 64 rows, how many distinct component…

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Q: Determine whether these statement forms are logically equivalent. In each case, construct a truth…

A: Boolean algebra is a branch of mathematics that is concerned with binary variables and operations on…

Q: Q4. Decide whether or not the following argument is valid by writing down truth tables (P₁ ^ P₂) →…

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Q: Identify if the argument is VALID or INVALID by analyzing the truth table test below: (L · (M ɔ S))…

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Q: Use the standard forms of valid and invalid arguments to determine the validity of the arguments.…

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Q: Assitance please: Given the following statements: Statement    1:    In    order    to    go    on…

A: Let, p : you  go    on    vacation q : you    must    be    vaccinated r : you    must  have    a…

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.