Department

PhilosophyCourse Code

PHIL 10Professor

Rick GrushChapter

2This

**preview**shows page 1. to view the full**5 pages of the document.**PHIL 10 – Textbook Notes – Chapter 2: Truth Functions and Truth Tables

2.1 Truth functional operators and truth tables

Valid argument: all true premises and false conclusion not possible

2.1.1 Introduction

Operators are truth-functional

2.1.2 Functions

Truth functions take truth values (T/F) as inputs, produce truth values as outputs (T/F)

2.2 Truth functions: conjunction and negation

Only have 2 truth values

1. True and false/T and F

Conjunction truth table

X Y X · Y

TTT

TFF

FTF

FFF

Conjunction Truth Function: conjunction is true when both conjuncts are true, false if

either/both conjuncts are false

Negation truth table

X Y

T F

F T

Negation Truth Function: negation is true if negated statement false, false if negated

statement true

2.3 Truth tables for compound statements, and the point of formal systems

~ (A • B)

list all combinations of T/F for the statements in the first two columns

use conjunction truth function to fill out column 3

use negation truth function to fill out column 4

A B A • B ~ (A • B)

T T T F

T F F T

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F T F T

F F F T

to make a truth table:

1. determine atomic statements

2. find intermediate compound statements between atomic statements

intermediate compound statements: statements created by separating the

operators

3. make a table with a row for every combination of truth values of atomic

statements, column for every statement, put statements at top of each column,

starting with atomic in alphabetical order

~ (~~S • ~~L)

atomic statements = S and L

intermediate compound statements: ~S, ~~S, ~L, ~~L, ~~S • ~~L, ~ (~~S • ~~L)

L S ~L ~~L ~S ~~S ~~S •

~~L

~ (~~S •

~~L)

TTFTFTTF

TFFTTFFT

FTTFFTFT

FFTFTFFT

2.4 Truth functions: disjunction and conditional

Exclusive or: either P or Q but not both, excludes possibility of both disjuncts being true

Inclusive or: true when either or both disjuncts are true

Inclusive Disjunction Truth Function: disjunction is true if either or both disjuncts is true,

false if and only if both disjuncts false

Inclusive disjunction truth function

X Y X v Y

TTT

TFT

FTT

FFF

Conditional Truth Function: conditional false if it has combination of true antecedent and

false consequent, all other conditions conditional is true

Conditional truth table

X Y X ⸧ Y

TTT

TFF

FTT

FFT

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