Kategorier: Alle - conclusion - negation - conditional - patterns

av Jaclyn Jones 14 år siden

230

Chapter 1 Summary

The text delves into the fundamental concepts of reasoning and logic, beginning with quantifiers which are key to understanding the scope of statements. Universal quantifiers pertain to terms like "

Chapter 1 Summary

Chapter 1 Summary

Reasoning and Logic

Valid

The conclusion follows unavoidably true from the hypothesis.

Biconditional

'P if, and only if, Q.'

Conclusion

The 'then ___' part of the if-then statement.

Hypothesis

The 'if___' part of the if-then statement.

Conditional

'If___, then ____' statement. Implication is the same as conditional statement.

Implication
Equivalence
Compound Statement

Connecting two statements together using the word 'and'.

Truth Tables

A table used to show all possible true-false patterns for statements.

Quantifiers
Existential

Words that refer to one or more, or possibly all, of the elements in a set; some, and there exists at least one.

Universal

Words that refer to each and every element in a set; all, every, and no.

Negation

A statement with the opposite truth value of the given statement.

Patterns

Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21,...,

Geometric

A geometric sequence is one in which each succesive term is obtained from its predecessor by multiplying by a fixed (constant) nonzero numer.

This number is called a ratio.

Arithmetic

An arithmetic sequence is one in which each succesive term from the second term on is obtained from the previous term by the addition or subtraction of a fixed (constant) number.

Strategies for Problem Solving

Write an Equation
Direct Reasoning
Indirect Reasoning
Work Backward
Guess and Check
Make a Diagram
Identify a Subgoal
Make a Table
Examine a Simpler Case
Examine a Related Problem