Q. 34.8( 4 Votes )

What is the funda

Answer :

Fundamental difference between Relation and Function:

Every function is a relation, but every relation need not be a function.


A relation f from A to B is called a function if


(i) Dom(f) = A


(ii) no two different ordered pairs in f have the same first component.


For. e.g.


Let A = {a, b, c, d} and B = {1, 2, 3, 4, 5}


Some relations f, g and h are defined as follows:


f = {(a, 1), (b, 2), (c, 3), (d, 4)}


g = {(a, 1), (b, 3), (c, 5)}


h = {(a, 1), (b, 2), (b, 3), (c, 4), (d, 5)}


In the relation f,



(i) Dom (f) = A


(ii) All first components are different.


So, f is a function.


In the relation g,


(i) Dom (g) ≠ A


So, the condition is not satisfied. Thus, g is not a function.


In the relation h,



(i) Dom (h) = A


(i) Two first components are the same, i.e. b has two different images.


So, h is not a function.


No, every relation is not a function.


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