An injective function is a one to one function . That is it will always map a particular element of N to a unique element. Clarly that is not the case here. for a counterexample, consider N = 4 for which the mapped function is 4 % 5 = 4 ( % stands for remainder) again consider N = 9 in which case, remainder = 9%5 = 4 Hence two elements of N point towards the same mapped element which is in violation of a one to one property. A surjective fnction is one in which all the elements of the codomain which is {0,1,2,3,4} here must be the mapped element for atleast one element belonging to the domain {N}. This is also clearly true, for any number of form 5n belonging to N where n is an integer the remainder is 0 for 5n+1, remainder is 1 for 5n+2, remainder is 2 for 5n+3, remainder is 3 for 5n+4, remainder is 4 Hence all the elements of the co domain occur atleast once which makes it a surjective function. Solution An injective function is a one to one function . That is it will always map a particular element of N to a unique element. Clarly that is not the case here. for a counterexample, consider N = 4 for which the mapped function is 4 % 5 = 4 ( % stands for remainder) again consider N = 9 in which case, remainder = 9%5 = 4 Hence two elements of N point towards the same mapped element which is in violation of a one to one property. A surjective fnction is one in which all the elements of the codomain which is {0,1,2,3,4} here must be the mapped element for atleast one element belonging to the domain {N}. This is also clearly true, for any number of form 5n belonging to N where n is an integer the remainder is 0 for 5n+1, remainder is 1 for 5n+2, remainder is 2 for 5n+3, remainder is 3 for 5n+4, remainder is 4 Hence all the elements of the co domain occur atleast once which makes it a surjective function..

1. An injective function is a one to one function . That is it will always map a particular element of
N to a unique element. Clarly that is not the case here. for a counterexample, consider N = 4 for
which the mapped function is 4 % 5 = 4 ( % stands for remainder) again consider N = 9 in which
case, remainder = 9%5 = 4 Hence two elements of N point towards the same mapped element
which is in violation of a one to one property.
A surjective fnction is one in which all the elements of the codomain which is {0,1,2,3,4} here
must be the mapped element for atleast one element belonging to the domain {N}.
This is also clearly true, for any number of form 5n belonging to N where n is an integer
the remainder is 0
for 5n+1, remainder is 1
for 5n+2, remainder is 2
for 5n+3, remainder is 3
for 5n+4, remainder is 4
Hence all the elements of the co domain occur atleast once which makes it a surjective function.
Solution
An injective function is a one to one function . That is it will always map a particular element of
N to a unique element. Clarly that is not the case here. for a counterexample, consider N = 4 for
which the mapped function is 4 % 5 = 4 ( % stands for remainder) again consider N = 9 in which
case, remainder = 9%5 = 4 Hence two elements of N point towards the same mapped element
which is in violation of a one to one property.
A surjective fnction is one in which all the elements of the codomain which is {0,1,2,3,4} here
must be the mapped element for atleast one element belonging to the domain {N}.
This is also clearly true, for any number of form 5n belonging to N where n is an integer
the remainder is 0
for 5n+1, remainder is 1
for 5n+2, remainder is 2
for 5n+3, remainder is 3
for 5n+4, remainder is 4

2. Hence all the elements of the co domain occur atleast once which makes it a surjective function.