/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 Give the negation of each statem... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 13

Give the negation of each statement. The city is large.

Short Answer

Expert verified
The city is not large.

Step by step solution

01

- Understand the Statement

The given statement is 'The city is large.' It is important to identify the main subject and predicate. Here, 'The city' is the subject and 'is large' is the predicate.
02

- Apply Negation

To negate the statement, introduce the word 'not' appropriately. The negation of 'The city is large' is 'The city is not large.'
03

- Verify the Negation

Ensure the negation makes sense and is grammatically correct. 'The city is not large' correctly negates the original statement.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

statement negation
Negation in logic is about reversing the truth value of a statement. If a statement is true, its negation is false, and vice versa. In our example, the statement 'The city is large' is an affirmative statement. To create its negation, we introduce the word 'not'. Thus, 'The city is not large' is the negation. In general, when you negate a statement, you are saying the opposite of what the original statement asserts.
For example:
  • Statement: 'The sky is blue.'
  • Negation: 'The sky is not blue.'
The process involves identifying the main components of the statement and appropriately inserting 'not' while ensuring grammatical correctness. This simple technique can be applied to a wide range of statements.
logical reasoning
Logical reasoning involves making deductions and deriving conclusions from a set of premises or statements. Negation is an essential tool in logical reasoning.
By understanding how to negate statements, we can form correct conclusions and counterarguments. For instance, if you know 'The city is large' is true, the statement 'The city is not large' must be false. Conversely, if 'The city is not large' is true, 'The city is large' must be false.
Logical reasoning allows us to work with these statements in arguments, proofs, and problem-solving.
Consider another example:
  • Statement: 'All birds can fly.'
  • Negation: 'Not all birds can fly.' (or equivalently, 'Some birds cannot fly.')
This negation can help you critically analyze information and arrive at well-reasoned conclusions.
predicate logic
Predicate logic is a form of logic where statements are expressed in terms of subjects and predicates. It extends propositional logic by dealing with predicates, which are properties or relations between subjects.
In our example, 'The city is large,' 'the city' is the subject, and 'is large' is the predicate.
Negating such a statement means applying the 'not' to the predicate, resulting in 'The city is not large.'
Predicate logic helps us analyze more complex statements involving variables and quantifiers.
For example:
  • Statement: 'All students are diligent.'
  • Negation: 'Not all students are diligent.' (which can also be stated as 'Some students are not diligent.')
Understanding predicate logic enhances our ability to interpret and manipulate logical statements in various contexts, from mathematics to computer science.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine if each conclusion follows logically from the premises and state whether the reasoning is inductive or deductive. Premise: If I buy a car, then it will be a Buick. Premise: If I receive a check from my father, then I will buy a car. Premise: I received a check from my father. Conclusion: I will buy a Buick.

Draw a line segment \(\overline{A B}\) approximately 2 inches in length and locate the midpoint of the segment by bisecting it.

Draw a line \(\ell\) and select two points \(P\) and \(Q\) on \(\ell\). Construct the perpendicular bisector of \(\overline{P Q}\) and locate the midpoint of \(\overline{P Q}\).

For problems 13-26, explain the reasoning in one or two complete sentences. If \(\angle A\) and \(\angle B\) are complementary, can \(\angle A\) and \(\angle B\) be vertical angles too?

Determine if each conclusion follows logically from the premises and state whether the reasoning is inductive or deductive. Premise: If you are a home buyer, then you make payments. Premise: Doug is a home buyer. Conclusion: Doug makes payments.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.