Let be an equivalence relation on a non-empty set

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

R

be an equivalence relation on a non-empty set

A

. Denote by

[a]

the equivalence class of an element

a\in A

. (i) State the property that describes the relationship between any two equivalence classes of

R

. (ii) Prove that, for any

a,b\in A

, either

[a]=[b]

[a]\cap[b]=\varnothing

. (iii) Explain briefly how this property ensures that the collection of all equivalence classes forms a partition of

A