Discrete math Lec 1

Proposition

A declarative statement that is either True (T) or False (F), but not both.

Backwards E (∃)

Stands for "There exists" (Existential Quantifier).

Upside down A (∀)

Stands for "For all" (Universal Quantifier).

Propositional Variables (Atoms)

Variables used to represent propositions (e.g., p, q).

Compound Proposition

A statement formed by combining one or more atoms using logical connectives.

Logical Connectives

Negation, Conjunction, Disjunction, Exclusive OR, Implication, Biconditional.

Negation (¬p)

"Not p"; converts the truth value to its opposite.

Conjunction (p ∧ q)

"p AND q"; True only when both p and q are True.

Disjunction (p ∨ q)

"p OR q" (Inclusive); True if at least one is True.

Exclusive OR (p ⊕ q)

"p XOR q"; True if exactly one is True, but not both.

Conditional Statement (p → q)

"If p, then q"; False ONLY if p is True and q is False. Vacuously True otherwise.

Biconditional Statement (p ↔ q)

"p if and only if q"; True if both have the same truth value.

Truth Table Rows

Always 2^k rows, where k is the number of propositional variables.

Truth Assignment

Assigning a truth value (T or F) to each atom in a compound proposition.

Tautology

A proposition that is always True.

Contradiction

A proposition that is always False.

Contingency

A proposition that is a mix of True and False.