MODULE 3-4

Propositional logic

is about reasoning with propositions.

These are sentences that can be assigned a truth value: true or false

atomic propositions

built from primitive statements, called __________ , by using propositional logical connectives.

propositional formulae

how to reason using schemes of propositions called

proposition

The basic concept of propositional logic.

is a sentence that can be assigned a unique truth value: true or false.

logical connectives

From primitive propositions one can construct compound propositions by using special words called

not

called negation, denoted ¬

and

called conjunction, denoted ∧ (or sometimes &);

or

called disjunction, denoted ∨;

if, then

called implication, or conditional, denoted →;

if and only if

called biconditional, denoted ↔.

conjunctions

In natural language grammar the binary propositional connectives, plus others like but, because, unless, although, so, yet, etc. are all called “_____________” because they “conjoin

propositional connectives

In logic we use the __________________ to connect propositions

proposition

is a declarative sentence that is either true or false

TRUE

(TRUE OR FALSE)

The sun is hot.

Is a example of proposition

TRUE

(TRUE OR FALSE)

The 1000th decimal digit of the number π is 9.

Is a example of proposition

FALSE

• The truth depends on who “she” is and who utters the sentence.

(TRUE OR FALSE)

She loves me.

Is a example of proposition

FALSE

(TRUE OR FALSE)

Are you bored?

Is a example of proposition

FALSE

(TRUE OR FALSE)

Please, don’t go away!

Is a example of proposition

TRUE

(TRUE OR FALSE)

The Earth is made of cheese

Is a example of proposition

FALSE

• not determined as long as the variable x is not assigned a value, integer or not

(TRUE OR FALSE)

x is an integer.

Is a example of proposition

FALSE

• assuming that it is true it truly claims that it is false – a contradiction; assuming that it is false, it falsely claims that it is false, hence it is not false – a contradiction

(TRUE OR FALSE)

This sentence is false.

Is a example of proposition

TRUE

(TRUE OR FALSE)

It is often not grammatically correct to read compound propositions by simply inserting the names of the logical connectives in between the atomic components

TRUE

(TRUE OR FALSE)

A proposition is a declarative sentence that is either true or false.