D logically says "For all $c$ there does not exist a value of $b$ such that $2\times b=c."$ It is easy to prove this false by counterexample. If $c=4,$ then a possible value for $b$ is $2,$ which contradicts the logic of the statement. Therefore, $\boxed{\text{D}}$ is false.

A) "Not all $c$ , such that some of $b$ satisfies $2b = c$ " means some (or no) $c$ and some $b$ makes this true, which is true. ex. $2*(2) = (4)$ .

B) "All of $c$ , such that some of $b$ satisfies $2b \neq c$ " means any $b$ can make this equation false for any $c$ , which is true. ex. $2b \neq 5$ for any integers $b$ .

C) "None of $b$ , such that all of $c$ satisfies $2b = c$ " means if $c$ changes, $b$ will not stay the same, which is true. (because $f(x) = 2b$ is a 1-by-1 function).

D) "All of $c$ , such that none of $b$ satisfies $2b = c$ " means every number $c$ can't be written in the form of $2b$ , which is false, because even number can be written as $2k, \forall k \in Z^{+} \cup$ { $0$ }.

Therefore, the answer is $\boxed{D}$ .~~~

My solution using C++

 #include<iostream.h>
 int main()
 {
 cout<<"All right, I am nuts. Sue me. Here's the solution, though -\n\n"<<endl;
 cout<<"A)\nNot for all (i.e. For some) c, there exists some b";
 cout<<" such that twice of b is c.\nThis is true.\n"<<endl;
 cout<<"B)\nFor all c, there exists some b such that twice of b";
 cout<<" is not c.\nThis is true.\n"<<endl;
 cout<<"C)\nThere does not exist any b such that for all c,";
 cout<<" twice of b comes out to be c.";
 cout<<"\nOR\n";
 cout<<"For any fixed value of b, \'2b = c\' is not true for ALL c.";
 cout<<"\nThis is true\n"<<endl;
 cout<<"D)\nFor all c, there does not exist any b such that twice of b is c.";
 cout<<"\nOR\n";
 cout<<"\'There exists some b such that twice of b is c.\' is false for all c.";
 cout<<"\nThis is FALSE.\n\n"<<endl;
 cout<<"So, answer (false) is D.";
 return(0);
 }