The Gateway to Computer Science Excellence
+2 votes
Let f : A → B be function, where A = {1,2,3,4,5,6} and B = {1,2,3,4,5}.

If f(1) = 4 then how many surjective (onto) functions are possible ?
in Set Theory & Algebra by Loyal (5.6k points)
edited by | 279 views

@Prince Sindhiya

type the questions instead of screenshots

@shaik i access GO most of the time from mobile phone and i am not good with latex symbols even many times i tried when i was a new user but it took around 45 mins to 1 hour in typing the solutions to answering and all screenshot i posted are visible so i started Posting questions by taking the screenshot
But from now onwards for simple question i will type the question
for solutions no need, atleast for questions you can do that, hardly it take 5 min...

click on fx button, there you will type, no need to manually write the latex code.

searching By images is more difficult when we are finding duplicates...
can you tell me that how to subscript and superscript ?

I didn't find that func button in this updated version

check this


Ohk fine :p

earlier it was bit easy because both function are very frequently use so sir make a separate  button for this two func

 btw thanks

1 Answer

+4 votes
Best answer

related theory

formula derivation is in given link

by Boss (10.2k points)
selected by
@gurdeep same solution is given for it

But i understood the second part that f(1) =4 that's why we have excluded that but why we are considering 4 in first part and why this 5Factorial is coming i wrote it's solution as 240 only please tell me the first part by explaining it a bit more

 Prince Sindhiya

F(1)=4 is given and set b contain 5 element 

now in set A we have total 6 element including 1 

means 5 element excuding 1 

given that 5 element in B 

it means both set have 5 ,5 element where 1 is already related to 4  

now in the remaining 5 element of A we have to relate every element of A only one element of B here we can not relate 2 element of A to the single element of B because it we do so than this will not satisfy onto property because  some element will left unrelated in B 

so first element of A can relate to 5 ways 

and second element of A can relate to 4 ways

3 rd element 3 ways 

4th  element 2 ways

5th  element  1 ways  

so total ways is 5!

so in this process

 (one thing you should note in this process 4 element of B is related to two different element of A  )


Gurdeep thnxx for such a beautifull solution

Gurdeep Saini

tell me one thing

we exclude (1) from A is understandable

but why you exclude (4) from B ??

for every element y in the codomain B of f there is at least one element x in the domain A

one of the element from A {2,3,4,5,6} can  map to to B (4) right ?? 


Prince Sindhiya  clear my doubt



element 1 of A already map to 4 of B  now we can ignore that elment 

and do the maping of rest 

we can ignore 1

but why we ignore 4 also ??

because if 4 have 2 image in domain..then there's  no problem right ???

I know I'm wrong....but I want clarify my doubt..that's why I asking question
because if 4 have 2 image in domain..then there's  no problem right ???

@magma this in included in first case

what I wanted to say is that

this is possible right ??


yes @magma this is possible 

but included in first case 

in the first case        1 element and one other of A related to 4 of B (shown by you in figure)

but in second case      only 1 element of A relate to the 4 element of B and rest elment of A relate to the remaining four element of B  


@Gurdeep Saini , great solution , so in this we have to take 2 cases, one with element 4 in the set B and one without element 4 in set B , because f(1)=4 , so element 4 from set B could be used or could not be used, so 2 cases.


@Gurdeep Saini

Good one :)


i request to the person who downvoted this  answer 

please tell me what is wrong so that i dont repeat this mistake in exam 


@Gurdeep Saini

who just down vote but didn't participate in the discussion, doesn't get this comment as notification


@Shaik Masthan he/she should give the reason what is wrong in this answer 

we can't do anything... it's his/her responsibility.... forget about it.. there is No problem with this solution
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,650 questions
56,242 answers
95,944 users