[Shivani Ramesh]

No the statement is false.

Let's take an example,

if we make a rule and declare that the difference between x and y is  divisible by 3 which makes an equivalence relation

so in this way we can partition many sets like

{0,3,6,9,12...............}

{1,4,7..................}

{2,5,8,11..............}

by this we cannot partition all the numbers because it is infinite

and we can get the equivalence relation back so this proves that the statement is false.

[Shivani Ramesh]

It is true because:

every equivalence relation is

-symmetric

-reflexive and

-transitive

so when we partition the sets they are reflexive, symmetric and transitive

 

[Shivani Ramesh]

• A point is equivalent only when it has 3 critical properties:
• symmetric(a~a)
  reflexive(a~b and b~a)
  transitive(a~b , b~c , c~a)
• We tell some points as same when we glue those points.
• When we glue these points in a certain manner we get a 3 dimensional figure.
• Congurence is equivalence
• It is reflexive as anything is congurent to itself.
• Suppose any number is congurent to another number it will be congurent to it.
• Since a~b,b~c,a~c.

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