Maths WorkshopMaths problems with full solutions

Relations

14 problems · Equivalence relations, equivalence classes, partial orders and partitions.

Ex.182Congruence is an equivalence relation
#relations #modular arithmetic
Relations
L1
L1
Ex.272Binary relations
#binary relation #definition #examples
Relations
High school
High school
Ex.273Reflexive relations
#reflexive #relation #definition
Relations
High school
High school
Ex.274Symmetric relations
#symmetric #relation #definition
Relations
High school
High school
Ex.275Transitive relations
#transitive #relation #definition
Relations
High school
High school
Ex.565Antisymmetric relations
#antisymmetric #relation #definition
Relations
High school
High school
Ex.566Equivalence classes
#equivalence class #congruence #quotient
Relations
High school
High school
Ex.567Equivalence relations
#equivalence relation #reflexive #symmetric #transitive
Relations
High school
High school
Ex.568Partial orders
#partial order #poset #subsets
Relations
L1
L1
Ex.1164Hasse diagram
#Hasse diagram #covering #poset
Relations
L1
L1
Ex.1165Equivalence classes form a partition
#partition #equivalence classes #proof
Relations
L1
L1
Ex.1166Partitions induce equivalence relations
#partition #equivalence #converse
Relations
L1
L1
Ex.1167Total orders
#total order #comparability #real numbers
Relations
L1
L1
Ex.1180Total orders
#total order #comparability #poset
Relations
L1
L1