# Equivalence relation: Quiz

Question 1: Two elements of the set are considered equivalent (with respect to the equivalence relation) ________ they are elements of the same partition.
Propositional calculusFirst-order logicIf and only ifLogical connective

Question 2: ________ is another name for a small category of this nature.
MonoidGroup (mathematics)Group actionGroupoid

Question 3: The empty relation R on a ________ set X (i.e.
Set theoryTopological spaceSet (mathematics)Empty set

Question 4: The possible equivalence relations on any set X, when ordered by set inclusion, form a ________, called Con X by convention.
Order theoryLattice (order)Complete latticeSemilattice

Question 5: The former structure draws primarily on ________ and, to a lesser extent, on the theory of lattices, categories, and groupoids.
Lie groupGroup (mathematics)Group theoryGeneral linear group

Question 6: Conversely, any surjection between sets determines a partition on its domain, the set of ________ of singletons in the codomain.
Image (mathematics)Function (mathematics)Set (mathematics)Set theory

Question 7: ________'s The Elements includes the following "Common Notion 1":
AnaxagorasEuclidArchimedesDemocritus

Question 8: In ________, an equivalence relation is, loosely, a relation that specifies how to partition a set such that every element of the set is in exactly one of the partitions and the union of all the partitions equals the original set.
Mathematical logicMathematicsGeometrySet theory

Question 9: "Is parallel to" on the set of subspaces of an ________.
Vector spaceAffine combinationAffine spaceMathematics

Question 10: Moving to groups in general, let H be a ________ of some group G.
SubgroupGroup homomorphismQuotient groupAbelian group