Suppose we have a function HALTS which when applied to any arbitrary function f and its arguments will say TRUE if function f terminates for those arguments and FALSE otherwise. Example, Given the following function definition.
FACTORIAL (N) = IF(N=0) THEN 1 ELSE N*FACTORIAL (N-1)
Then HALTS(FACTORIAL 4) = TRUE and HATS(FACTORIAL - 5) = FALSE

Let us define the function FUNNY(f) = IF HALTS(ff) THEN not(ff) ELSE TRUE
(a) Show that FUNNY terminates for all functions f.
(b) Use (a) to prove (by contradiction) that it is not possible to have a function like HALTS which for arbitrary functions and inputs says whether it will terminate on that input or not.

In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known whether @anand was a knight or a knave. A crack team, headed by Inspector Chitra, rounded up three suspects and interrogated them.
The first interrogation went as follows.
Chitra : What do you know about @anand?
Suspect 1 : @anand once claimed that I was a knave.
Chitra : Are you by any chance @anand?
Suspect 1 : Yes.
The second interrogation:
Chitra : Have you ever claimed you were @anand?
Suspect 2 : No.
Chitra : Did you ever claim you are not @anand?
Suspect 2 : Yes.
The third suspect arrived with a defense lawyer (also on Twitter):
Lawyer : My client is indeed a knave, but he is not @anand.
Suspect 3 : My lawyer always tells the truth.
Which of the above suspects are innocent, and which are guilty?
Explain your reasoning.

What is the output of the following program?
abstract class Sum
{
public abstract int sumOfTwo(int n1, int n2);
public abstract int sumOfThree(int n1, int n2, int n3);
public void disp() {
System.out.println(Method of class Sum);
}
}
class DemoAbstract[] extends Sum
{
public int sumOfTwo(int num1, int num2)
{
return num1+num2;
public int sumOfThree(int num1, int num2, int num3)
{
return num1 + num2 + num3;
}
public static void main(String args[]) {
Sum.obj = new DemoAbstract1();
System.out.println(obj.sumOfTwo(3, 7));
System.out.println(obj.sumOfThree(4, 3, 19));
obj.disp();
}
}