Chapter 1.1 Statements, Symbolic Representation, Tautologies

Logic

foundation for the organized, careful method of thinking that characterizes any reasoned activity

The study of reasoning –

specifically concerned with whether something is true or false

Formal logic focuses on the _________ as opposed to the content of any particular statement

relationship between statements

Statement (proposition)

A sentence that is either true or false, but not both

Truth value of a statement

▪ True, T, 1

▪ False, F, 0

Λ

and

V

or

→:

implies

←→

equivalent

‘

negation

Conjunction (Λ)

▪ A Λ B is TRUE when both A and B are true

▪ A Λ B is FALSE when at least one of A or B is false

Disjunction (V)

A V B is TRUE when at least one of A or B is

true

▪ A V B is FALSE when both A and B are false

Implication (→)

if a, then b

Implication Statements

▪ A → B is FALSE when A is true and B is false

▪ A → B is TRUE otherwise

Equivalence (←→)

A ←→ B stands for (A → B) Λ (B → A)

TRUE: Both A and B have the same truth values

FALSE: A and B have different truth values

Negation (’)

opposite truth value