A logic problem: Who is the killer??? (Do you Have a Mr:Sherlock inside you?)

For most of the time in our life we are busy with our day today works.May be with our studies or with our job. So here  I present you a small problem which is not related to any of those,but will need some brain cells to provide the correct  answer.So here goes the Adventure.

There were five people travelling in a train and they are named A,B,C,D and E. Here A,C and E are men and B,D are women. Suddenly train passed through a tunnel and when it emerges E was found dead.

And a detective came to the place and talk to other for passengers to get evidence.This is the result he got after talking to remaining four people.

A Said

I'm innocent : B was talking to E when the train was passing though the tunnel

B Said

I'm innocent : I was not talking to E when the train was passing through the tunnel.

C Said

I'm innocent : D committed the murder.

D said

I'm innocent :One of the men committed the murder.

You can see these four people are making eight statements,two by each person.And the detective could find out that four of these statements are true. And four of them are false.But he doesn't know which one of them are true and which are false.And he also got to know that only ONE person did the crime.Assuming you are the detective try to find out the killer?

                          

These are small logic problems which can be easily solved by doing some rough works.And these kind of problems are belong to the area called discrete mathematics .Try To Answer without help .I will post my answer Later. :).