Question

a library has two kind of employees.A person from the first kind always tells truth while the other person always lies.when you visit library to find weather Discrete Mathematics book is available,person of library at counter Mr. X answers as "Discrete Mathematics book is available if and only if I always tell truth".How will you confirm weather the book is available or not?

Answer 1

We can confirm by asking the other employee that if i ask X then will he say that you speak truth?

If the other employee is a liar then he will not say No as the X will tell the truth and say No (that the other employee does not say truth)  but the other employee says the opposite and will say Yes.
So, if the other employee is a liar he will say Yes.

Now if the other employee always says truth, he knows that X will tell lie and say that he does not speak truth.
So if the other employee always says truth he will say No.

Now the book is only available if the other employee is a liar and X speaks truth. So if the other employee says Yes to the question, it will be proved that he is a liar and the books are available while if he says No then he always says truth and X is a liar and the books are not available. 

Hope that helps !!