Answer
T: Z+ → D
T (n) = the set of all of the positive divisors of n.
a) one to one: True
Proof :
let's assume that p and q have the same image such that T(p) = T(q)
T(p) and T(q) sets have the largest integer divisor let it be X, now since they have the same image that means they have the same X and the largest divisor of a positive integer is the integer itself hence p= q = X.
b) onto : False, counterexample {1,2,3} $\in$ D
but there is no positive integer with {1,2,3} as its divisor since 3 is a prime and 6 Is missing itself from the set.
Work Step by Step
T: Z+ → D
T (n) = the set of all of the positive divisors of n.
a) one to one: True
Proof :
let's assume that p and q have the same image such that T(p) = T(q)
T(p) and T(q) sets have the largest integer divisor let it be X, now since they have the same image that means they have the same X and the largest divisor of a positive integer is the integer itself hence p= q = X.
b) onto : False, counterexample {1,2,3} $\in$ D
but there is no positive integer with {1,2,3} as its divisor since 3 is a prime and 6 Is missing itself from the set.