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Chapter 3: Problem 56

Let \(p\) and \(q\) represent the following simple statements: \(p\) : Romeo loves Juliet. \(q\) : Juliet loves Romeo. Write each symbolic statement in words. \(\sim p \vee q\)

Short Answer

Expert verified
The symbolic statement \(\sim p \vee q\) translates into words as 'It is not true that Romeo loves Juliet or Juliet loves Romeo'.

Step by step solution

01

Identify the logic symbols

The symbols in the given logical statement are as follows: \(\sim\) which represents negation, \(\vee\) which represents the logical OR. Here, \(p\) represents 'Romeo loves Juliet' and \(q\) represents 'Juliet loves Romeo'.
02

Translate each part of the statement

Let's start by translating each part of the statement. \(\sim p\) would mean 'It is not true that Romeo loves Juliet'. \(q\) corresponds to 'Juliet loves Romeo'.
03

Combine the parts together

Now, \(\sim p \vee q\) translates to 'It is not true that Romeo loves Juliet or Juliet loves Romeo'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Logical Negation
Logical negation is a fundamental concept in mathematics and symbolic logic. It refers to the operation of inverting the truth value of a given statement. If we have a statement, say 'Romeo loves Juliet' which is represented symbolically as 'p', then the negation of this statement, written as '
Logical Disjunction
Equivalent to the word 'or' in everyday language, logical disjunction is represented by the symbol '
Symbolic Logic
Symbolic logic, also known as formal logic, is the study of symbols and the rules for their use in the form of logical expressions. It enables the representation of complex statements and the derivation of conclusions from them through rigorous methods. It employs a variety of symbols to represent logical operations and relationships, such as ' . Understanding the use of these symbols and how to interpret statements in symbolic logic is crucial in fields such as mathematics, computer science, and philosophy.

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Most popular questions from this chapter

Conservative commentator Rush Limbaugh directed this passage at liberals and the way they think about crime. Of course, liberals will argue that these actions [contemporary youth crime] can be laid at the foot of socioeconomic inequities, or poverty. However, the Great Depression caused a level of poverty unknown to exist in America today, and yet I have been unable to find any accounts of crime waves sweeping our large cities. Let the liberals chew on that. (See, I Told You So, p. 83) Limbaugh's passage can be expressed in the form of an argument: If poverty causes crime, then crime waves would have swept American cities during the Great Depression. Crime waves did not sweep American cities during the Great Depression. \(\therefore\) Poverty does not cause crime. (Liberals are wrong.) Translate this argument into symbolic form and determine whether it is valid or invalid.

In Exercises 15-42, translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If it is cold, my motorcycle will not start. My motorcycle started. \(\therefore\) It is not cold.

In Exercises 43-50, use the standard forms of valid arguments to draw a valid conclusion from the given premises. If a person is a chemist, then that person has a college degree. My best friend does not have a college degree. Therefore, ...

Use Euler diagrams to determine whether each argument is valid or invalid. All physicists are scientists. All scientists attended college. Therefore, all physicists attended college.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If I am at the beach, then I swim in the ocean. If I swim in the ocean, then I feel refreshed. \(\therefore\) If I am at the beach, then I feel refreshed.
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