Answer:
(a) Not a function, because a string can be assigned to more than one value.
(b) Function
(c) Not a function, because the function does not assign an integer to every string.
Step-by-step explanation:
Definition:
A function f from A to B has the property that has each element of A has been assigned to exactly one element of B.
Solution
A =Set of all bits strings
B= Z
(a) Given: f(S) ={position of a 0 bit in S}
f is not a function,because a string can be assigned to more than one value.
for example if S = 001, then f(S) =1 and f(S) =2,because S =001
contain a 0 in the first and second position.
Moreover there are also strings that do not get assign to an integer.For example,the string S= 111111 does not get assign by f,because S does not contain any 0's .
b) Given:f(S) ={number of 1 bits in S}
f is defined for all strings and the action f maps every element of A to exactly one element in Z,thus f is a function.
c)Given:
f(S) =i if the ith bit of S is the first 1 in the string
f(S)= 0 if S is the empty string
f is not a function because the string does not assign an integer to every string. More precisely,no integer are assigned to all string not containing a 1.
For example:
if S=00111,then f(S) =3.
if S=000000,then f(S) is not defined.
