Discrete Structures First Sem

Discrete Mathematics

a branch of mathematics involving discrete elements that uses algebra and arithmetic

Mathematical Statement

a set of words that can be considered true or false

Statement Notation

single letter

Atomic Statement

simple declarative sentence which can be either true or false

Atomic Statement Characteristics

Indivisibility, Truth Value, No Logical Operators, Simplicity, No Quantifiers

Molecular Statement

multiple atomic statements with logical operators

Conjunction

Combines two statements and true only if both statements are true

Disconjunction

Combines two statements and true if at least one statement is true

Implication

states that if one statement is true, then another statement must also be true, often expressed as "if… then…"

Negation

Reverses truth value of statement

Biconditional

True if both statements are either true or false

Parentheses

used to group statements and clarify order of operations

Logical Connectives

operators that are used to build molecular statements

Binary Connective

logical connective that connects two statements

Unary Connective

logical connective that applies to a single statement

Propositional Variables

variables that represent proposition in statements

conjuction symbol

p∧q

p∨q

disconjunction (symbol)

p→q

implication (symbol)

p↔q

biconditional (symbol)

¬p

negation (symbol)

Truth Table for Conjunction

Truth Table for Disconjunction

Truth Table for Implication

Truth Table for Biconditional