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Logic

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Created on December 5, 2021

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Transcript

TRAVEL GUIDE

Logic statement and QuantifiersTruth Tables and Tautologies

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Visiting Cordoba

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Examples

Logic in Math

logic Statement

Logic

What is Logic?

What is Logic in math?

example

use the two of the statements provided to form a COMPOUND STAtement using eACH OF the given connectives:

a. andb. or c. but d. if, then

Mathematics is a mental exercise.Push-ups are physical exercise. I will exercise.

Compound Statements

component statements

The statements making up the compound statement are called the component statements

may be formed by combining two or more statements

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Compound Statement

Components Statements

Connectives

Examples

eXamples

  • The earth revolves around the sun
  • The sun revolves around the earth
  • 1 + 2 = 3
  • How do you spell your name?
  • This sentence is false
  • Allen is not good student

Determine wether each sentence is a statement.

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Example: Compound Statements

Decide whether each statement is Compound. a. If Amanda said it, then it must be true. b. The gun was made by Smith and Wesson.

WHAT IS NEGATIONS

In Mathematics, the negation of a statement is the opposite of the given mathematical statement. Thus, if the given statement is true, then the negation of the given statement is false. It is observed that the “negation of the negated sentence is the original sentence”

Symbols

Map

Ex.

Logical Symbols

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WHAT IS QUANTIFIERS

Quantifiers are words, expressions, or phrases that indicate the number of elements that a statement pertains to. In mathematical logic, there are two quantifiers: 'there are Universal and existential quantifiers.

Universal Quantifiers

Existential Quantifiers

Example

Example The sentence "Max has a car." is a statement; the negation of this statement is "Max does not have a car" The negation of a true statement is false and the negation of a false statement is true.

Places of interest

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WHAT IS A TRUTH TABLE?

a List of all possible scenarios and the resulting truth values.

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TAUTOLOGY

A statement that is always true, no matter what the truth values of the components, is called a tautology. They may be checked by forming truth tables.

Example

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THANKS!

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