Sets, Logic & Proofs
Set operations, logical connectives, truth tables, proof techniques, and foundational reasoning.
Bounds, Intervals & Ordering9
Upper/lower bounds, bounded sets, intervals, and ordering concepts
Logic & Proof25
Conditional statements, proof methods, logical connectives, and quantifiers
Number Systems & Properties16
Algebraic properties, number classifications, and equivalence relations
Set Theory19
Sets, set operations, Venn diagrams, and set notation
All Sets, Logic & Proofs Terms A–Z (69)
- Additive Property of Equality
- Algebraic Numbers
- Associative
- Axiom
- Bounded Set of Geometric Points
- Bounded Set of Numbers
- Cardinality
- Commutative
- Complement of a Set
- Conclusion
- Conditional
- Conjecture
- Conjunction
- Continuous
- Contrapositive
- Converse
- Corollary
- Countable
- Countably Infinite
- Counterexample
- Discrete
- Disjunction
- Element of a Set
- Empty Set
- Equivalence Properties of Equality
- Equivalence Relation
- Exclusive
- Exclusive or
- Finite
- Googol
- Googolplex
- Hypothesis
- if and only if
- Inclusive
- Inclusive or
- Induction
- Infinite
- Infinitesimal
- Infinity
- Intersection
- Inverse of a Conditional
- Lemma
- Lower Bound of a Set
- Modus Ponens
- Modus Tolens
- Multiplicative Property of Equality
- Partition of a Set
- Postulate
- Proof by Contradiction
- Proper Subset
- Properties of Equality
- QED
- Reflexive Property of Equality
- Set
- Set Braces
- Set Subtraction
- Subset
- Superset
- Symmetric Property of Equality
- Theorem
- Transcendental Numbers
- Transitive Property of Equality
- Transitive Property of Inequalities
- Trichotomy
- Unbounded Set of Numbers
- Uncountable
- Union
- Upper Bound of a Set
- Venn Diagrams
Frequently Asked Questions
What is mathematical logic?
Mathematical logic is the study of formal reasoning. It uses symbolic notation to represent statements and their logical relationships, including conjunction (AND), disjunction (OR), negation (NOT), implication (IF...THEN), and biconditional (IF AND ONLY IF).
What is a mathematical proof?
A mathematical proof is a rigorous argument that establishes the truth of a statement using logical deduction from axioms and previously proven results. Common proof techniques include direct proof, proof by contradiction, proof by induction, and proof by contrapositive.