Discrete Mathematics Lecture Notes

A series of vocabulary flashcards based on the key concepts from the lecture notes on Discrete Mathematics.

Proposition

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

Truth Value

The truth (T) or falsity (F) of a proposition.

Negation

An operation that negates a proposition, indicating that it is not the case that the proposition holds.

Conjunction

The logical connective 'and', denoted by p ∧ q, which is true only when both propositions are true.

Disjunction

The logical connective 'or', denoted by p ∨ q, which can be inclusive (true if at least one is true) or exclusive (true if exactly one is true).

Conditional Statement

A statement of the form p → q, which asserts that q is true if p is true.

Biconditional Statement

A statement of the form p ↔ q, which indicates that p is true if and only if q is true.

Contrapositive

The proposition ¬q → ¬p, which is logically equivalent to the original conditional statement p → q.

Converse

The proposition q → p, which is derived by swapping the hypothesis and conclusion of the original conditional statement.

Inverse

The proposition ¬p → ¬q, which is derived by negating both the hypothesis and conclusion of the original conditional statement.