Equivalence classes of equivalence relation

Assignment Help Mathematics

Reference no: EM13132405

Modern Algebra

Set Theory (II)

Equivalence Classes of an Equivalence Relation

The distinct equivalence classes of an equivalence relation on a set A provide us with a decomposition of A as a union of mutually disjoint subsets.

Conversely, given a decomposition of A as a union of mutually disjoint, nonempty subsets, we can define an equivalence relation on A for which these subsets are the distinct equivalence classes.

Or, An equivalence relation over a set induces a partition of the set. Conversely, a partition of a set defines an equivalence relation.

Reference no: EM13132405

Questions Cloud

Variable utility cost per unit : Conan Company's monthly activity level ranged from a low of 17,000 units in May to a high of 26,000 units in October. Average production was 20,000 units per month. Utilities cost was $8,250 in May and $10,500 in October. The variable utility cost..

Expense warrenty accrual method : Record any necessary journal entries in 2010, applying the expense warrenty accrual method.

How much sulfuric acid can be produced : Sulfur trioxide dissolve in water, producing H2SO4. How much sulfuric acid can be produced from 13.5 mL of water and 26.1g of SO3?

What are the molecular weights of ether and dimethylether : What are the molecular weights of ether and dimethylether? Are they isomers of each other or is each an isomer of something else? Why are there significant differences in their chemical and physical properties?

Equivalence classes of equivalence relation : The distinct equivalence classes of an equivalence relation on a set A provide us with a decomposition of A as a union of mutually disjoint subsets. Conversely, given a decomposition of A as a union of mutually disjoint, nonempty subsets, we can d..

What is the substance : A liquid unknown was found to be insoluble in water and soluble in cyclohexane and alcohol; the unknown was found to have a boiling point of 58 degrees C at 670mm Hg

Molecule be made out of a methanol or ethanol molecule : Can an ether molecule be made out of a methanol or ethanol molecule? Why or why not? What is the structure for 1-Octanol & Propane-1,2,3-triol?

Investment using the equity method : What amount of unrelaized gross profit must Panner defer in reporting this investment using the equity method?

Explain what is the structure for hexadecanol : What is the structure for hexadecanol?, What would explain why it is a solid, rather than a liquid?, How are ethanol, 1-octanol, propane-1,2,3-triol, and hexadecanol similar to their corresponding hydrocarbons (ethane, octane, propane, & hexadecan..

User Account

All Pages