Discrete Structures 1 - Propositional Logic

Flashcards on Propositional Logic

Logic

A particular mode of reasoning viewed as valid or faulty.

Proposition

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

Simple Proposition

A proposition that cannot be further subdivided.

Compound Proposition

A proposition formed when two or more atomic propositions are combined using logical connectives.

Propositional Logic

A branch of mathematical logic that studies the logical relationships between propositions connected via logical connectives.

Propositional Variables

Variables that represent propositions (p, q, r, s, …).

Negation

NOT: symbolized by ¬

Conjunction

AND: symbolized by ∧

Disjunction

OR: symbolized by v

Conditional (Implication)

If, then: symbolized by →

Biconditional

if and only if

Conditional Statements

The proposition “if p, then q. ” p is called the hypothesis (or antecedent or premise)

Converse

Given a conditional statement p → q, then the q → p

Inverse

Given a conditional statement p → q, then the ¬p → ¬q

Contrapositive

Given a conditional statement p → q, then the ¬q → ¬p