reflexive means a is in relation with itself.

 

symmetric means, if a is in relation with b then b is also in relation will a.

 

transitive means if a is in relation with b and b is in relation with c .. it implies

 

that a is also in relation with c.

 

And a relation which is ref,sym, and trans is called an equivalence relation.

 

clearly similarity is an equivalence relation ..

First u must understand what is a relation.

 

A relation is subset of the cross product of 2 non empty sets A & B.

 

eg Set A = {1,2} and B = {a,b}

 

Then A cross B is a set C = { (1,a) ; (2,a) ; (1,b) ; (2,b) } A relation is a subset of the set C.

 

A reflexive relation is one which has (x,x) for all x belonging to sets A and B.

eg.

A cross A = {(1,1); (2,2) ; (1,2) }

A symmetric relation is one in which a set {x,y} is there and also {y,x} for all x belonging to first set and all y belonging to second set.

 

eg. A relation on sets A and B = { (1,1) ; (1,2) ; (2,1) ; (2,2)}

 

is symmetric as for (1,2) there is (2,1)

for (1,1) there is (1,1) for (2,2) there is (2,2)

 

A transitive relation is:

 

If (a,b) and (b,c) are present in a relation and (a,c) is also present for all a,b,c belonging to a relation then it is transitive in nature

 

For more info read Class 12 NCERT. It is an excellent book to understand basics of relations and functions.

 

 

Edit: An equivalence relation is one which is reflexive, symmetric and transitive in nature.