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Set	A collection of distinct objects		math-sets-logic
Element (member)	An object that is in a set		math-sets-logic
Empty set	The set with no elements, written ∅ or { }		math-sets-logic
Subset	A set whose elements are all in another set		math-sets-logic
Proper subset	A subset that is not the whole set		math-sets-logic
Union (A ∪ B)	Elements in A or B or both		math-sets-logic
Intersection (A ∩ B)	Elements in both A and B		math-sets-logic
Complement (A′)	Elements in the universal set that are not in A		math-sets-logic
Universal set	The set of everything under consideration		math-sets-logic
Disjoint sets	Sets with no elements in common		math-sets-logic
Cardinality	The number of elements in a set, written |A|		math-sets-logic
Roster form	Listing the elements: {1, 2, 3}		math-sets-logic
Set-builder notation	{x | x > 2} means all x such that x is greater than 2		math-sets-logic
Venn diagram	Overlapping circles showing how sets relate		math-sets-logic
Cardinality of a union	|A ∪ B| = |A| + |B| − |A ∩ B|		math-sets-logic
If A = {1,2,3} and B = {3,4}, A ∪ B	{1, 2, 3, 4}		math-sets-logic
If A = {1,2,3} and B = {3,4}, A ∩ B	{3}		math-sets-logic
Number of subsets of a set with n elements	2ⁿ		math-sets-logic
Number of subsets of {a, b, c}	8		math-sets-logic
Is ∅ a subset of every set?	Yes		math-sets-logic
Natural numbers symbol	ℕ		math-sets-logic
Integers symbol	ℤ		math-sets-logic
Rational numbers symbol	ℚ		math-sets-logic
Real numbers symbol	ℝ		math-sets-logic
Statement (proposition)	A sentence that is either true or false		math-sets-logic
Negation	The statement with the opposite truth value (not P)		math-sets-logic
Conjunction	P and Q; true only when both are true		math-sets-logic
Disjunction	P or Q; true when at least one is true		math-sets-logic
Conditional	If P then Q; false only when P is true and Q is false		math-sets-logic
Hypothesis	The 'if' part of a conditional		math-sets-logic
Conclusion	The 'then' part of a conditional		math-sets-logic
Converse	Swap the parts: if Q then P		math-sets-logic
Inverse	Negate both parts: if not P then not Q		math-sets-logic
Contrapositive	Swap and negate: if not Q then not P; same truth as the original		math-sets-logic
Biconditional	P if and only if Q; true when both have the same truth value		math-sets-logic
Truth table	A table listing the truth value of a statement for every case		math-sets-logic
Tautology	A statement that is always true		math-sets-logic
Contradiction	A statement that is always false		math-sets-logic
De Morgan's law 1	not (P and Q) is the same as (not P) or (not Q)		math-sets-logic
De Morgan's law 2	not (P or Q) is the same as (not P) and (not Q)		math-sets-logic
Counterexample	An example showing a statement is false		math-sets-logic
Direct proof	Proving a statement by a chain of logical steps from facts		math-sets-logic
Proof by contradiction	Assume the opposite and show it leads to something impossible		math-sets-logic
Proof by induction	Show it for a first case, then show each case leads to the next		math-sets-logic
Inductive reasoning	Reaching a general rule from patterns		math-sets-logic
Deductive reasoning	Reaching a conclusion that must follow from given facts		math-sets-logic
Axiom	A basic statement accepted without proof		math-sets-logic
Lemma	A small proven result used to prove a bigger one		math-sets-logic
Corollary	A result that follows easily from a theorem		math-sets-logic
Q.E.D.	Latin 'quod erat demonstrandum': which was to be shown		math-sets-logic
Necessary condition	Something that must be true for another thing to be true		math-sets-logic
Sufficient condition	Something that, if true, guarantees another thing		math-sets-logic
Quantifier ∀	For all		math-sets-logic
Quantifier ∃	There exists		math-sets-logic
Boolean value	True or false, often written 1 or 0		math-sets-logic
AND gate output	1 only if both inputs are 1		math-sets-logic
OR gate output	1 if at least one input is 1		math-sets-logic
NOT gate output	The opposite of the input		math-sets-logic
Binary number system	Base 2, using only digits 0 and 1		math-sets-logic
Binary 101 in decimal	5		math-sets-logic
Decimal 10 in binary	1010		math-sets-logic
Binary 1111 in decimal	15		math-sets-logic