Sets, Logic & Proofs
Sets, logic, and proofs provide the formal language and reasoning methods used throughout mathematics. This section covers set operations, logical connectives, truth tables, proof techniques, and foundational concepts like quantifiers and equivalence relations.
Key Concepts
Set-builder notation is a compact way to describe a set by stating a rule or condition that its elements must satisfy...
Commutative is a property of an operation where the order of the inputs does not change the result. An operation ∗ is...
An identity is an equation or inequality that is true for all permissible values of its variables. Unlike a condition...
Properties of Equality are the fundamental rules that allow you to manipulate both sides of an equation in the same w...
Properties of Equality are the fundamental rules that allow you to manipulate both sides of an equation in the same w...
Properties of Equality are the fundamental rules that allow you to manipulate both sides of an equation in the same w...
Proof by contradiction is a method of mathematical proof in which you assume the opposite of what you want to prove, ...
Proof by contradiction is a method of mathematical proof in which you assume the opposite of what you want to prove, ...
Equivalence Properties of Equality are the three fundamental properties — reflexive, symmetric, and transitive — that...
Inequality rules are the algebraic properties that govern how you can manipulate inequalities while preserving the di...
Compression of a geometric figure is a transformation that shrinks every point of the figure toward a fixed center po...
Mutually exclusive events are two or more events that cannot occur at the same time. If one event happens, the other ...
All Sets, Logic & Proofs Terms (103)
- Additive Inverse of a Number
- Additive Property of Equality
- Aleph Null
- Algebraic Numbers
- Algorithm
- Associative
- Axiom
- Biconditional
- Bounded Set of Geometric Points
- Bounded Set of Numbers
- Cardinal Numbers
- Cardinality
- Closed Interval
- Commutative
- Complement of a Set
- Conclusion
- Conditional
- Conjecture
- Conjunction
- Continuous
- Contraction of a Geometric Figure
- Converse
- Corollary
- Countable
- Countably Infinite
- Counterexample
- Counting Numbers
- Discrete
- Disjoint Sets
- Disjunction
- Element of a Set
- Empty Set
- Equality, Properties of
- Equivalence Properties of Equality
- Equivalence Relation
- Exclusive (interval)
- Exclusive or
- Finite
- Googol
- Googolplex
- Half-Closed Interval
- Hypothesis
- Identity (Equation)
- Identity of an Operation
- Inclusive (interval)
- Inclusive or
- Indirect Proof
- Induction
- Inequality
- Inequality Rules
- Infinite
- Infinitesimal
- Infinity
- Integers
- Integral
- Intersection
- Interval
- Interval Notation
- Inverse
- Inverse of a Conditional
- Irrational Numbers
- Lemma
- Lower Bound
- Modus Ponens
- Modus Tolens
- Multiplicative Property of Equality
- Mutually Exclusive
- Negative Number
- Nonnegative
- Nonnegative Integers
- Nonreal numbers
- Nontrivial
- Nonzero
- Odd Number
- Open Interval
- Ordinal Numbers
- Positive Number
- Postulate
- Proper Subset
- QED
- Rational Numbers
- Real Numbers
- Reflexive Property
- Set
- Set Braces
- Set Subtraction
- Set Union
- Set-Builder Notation
- Solution Set
- Subset
- Superset
- Symmetric Property
- Theorem
- Transcendental Numbers
- Transitive Property of Equality
- Transitive Property of Inequalities
- Trichotomy
- Trivial
- Unbounded Set of Numbers
- Uncountable
- Uniform
- Upper Bound
- Venn Diagrams