Boolean Logic and Sets (Vocabulary from Lecture video)

Vocabulary flashcards covering key concepts from the video: logical connectives, implications, De Morgan’s laws, sets and membership, Venn diagrams, order of operations, and some course logistics from the lecture.

Truth table

A chart showing the truth values of a logical expression for all possible truth values of its variables.

Implication (If-Then)

A logical statement of the form p -> q, meaning if p is true then q is true; true except when p is true and q is false.

Converse

The implication where the antecedent and consequent are swapped (q -> p) of the original p -> q.

Inverse

The implication formed by negating both parts of p -> q: not p -> not q.

Contrapositive

The implication formed by negating and swapping: not q -> not p; logically equivalent to the original p -> q.

De Morgan’s laws

Rules: not (p and q) ≡ (not p) or (not q) and not (p or q) ≡ (not p) and (not q).

Logical equivalence

Two statements that have the same truth value for all possible inputs; they are true in exactly the same cases.

Conjunction

The AND operator; true only when both operands are true.

Disjunction

The OR operator; true if at least one of the operands is true.

Negation

The NOT operator; a unary operator that inverts a truth value (true becomes false, false becomes true).

XOR (exclusive or)

An OR-like operator that is true only when exactly one of the operands is true.

Arity

The number of inputs an operator takes; e.g., NOT has arity 1, AND/OR/IMPLICATION have arity 2.

Unary vs. Binary operators

Unary operators take one input (e.g., NOT); binary operators take two inputs (e.g., AND, OR, IMPLICATION).

Set

A collection of unique elements where order does not matter.

Element of a set (membership)

An object that belongs to a set, often denoted as x ∈ S.

Subset

A set contained within another set; every element of the subset is also in the superset.

Intersection

Elements that are common to two sets; the overlap in a Venn diagram.

Venn diagram

A visual representation of sets using overlapping circles to show relationships like intersection and subset.

Order of operations (Boolean logic)

Rules for evaluating expressions, typically: parentheses, NOT, AND, OR, XOR, and IMPLICATION, in a defined precedence.

Boolean logic

A branch of logic using truth values (true/false) to form and evaluate logical expressions.