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2. List of set identities and relations - Wikipedia

   en.wikipedia.org/wiki/List_of_set_identities_and...

   This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.

3. Equality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Equality_(mathematics)

   In some cases, one may consider as equal two mathematical objects that are only equivalent for the properties and structure being considered. The word congruence (and the associated symbol ≅ {\displaystyle \cong } ) is frequently used for this kind of equality, and is defined as the quotient set of the isomorphism classes between the objects.

4. Equivalence class - Wikipedia

   en.wikipedia.org/wiki/Equivalence_class

   The set of all equivalence classes in with respect to an equivalence relation is denoted as /, and is called modulo (or the quotient set of by ). [3] The surjective map x ↦ [ x ] {\displaystyle x\mapsto [x]} from X {\displaystyle X} onto X / R , {\displaystyle X/R,} which maps each element to its equivalence class, is called the canonical ...

5. Equivalence relation - Wikipedia

   en.wikipedia.org/wiki/Equivalence_relation

   Equality is also the only relation on a set that is reflexive, symmetric and antisymmetric. In algebraic expressions, equal variables may be substituted for one another, a facility that is not available for equivalence related variables. The equivalence classes of an equivalence relation can substitute for one another, but not individuals ...

6. Algebra of sets - Wikipedia

   en.wikipedia.org/wiki/Algebra_of_sets

   The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".

7. Big 12 fines Arizona State $25,000 for premature field storm ...

   www.aol.com/sports/big-12-fines-arizona-state...

   Arizona State has been fined for the chaotic end to its win over BYU on Saturday. The Big 12 said Tuesday that it was fining the school $25,000 and issuing a public reprimand for the field storm ...