Who knocked over the monitor?

Melissa and Jessica were working on the computer along with their friends Sandy and Nicole.  Suddenly, I heard a crash and then lots of shouts.  I rushed in to find out what was going on, finding the computer monitor on the ground, surrounded with broken glass!  Sandy and Jessica spoke almost at the same time:

Jessica saying, "It wasn't me!"

Sandy saying, "It was Nicole!"

Melissa yelled, "No, it was Sandy!"

With a pretty straight face Nicole said, "Sandy is a liar."

Only one of them was telling the truth, so who knocked over the monitor? 

Find here who did it! 

Source 
  

Person Who knocked Over Monitor!

What's the entire matter? 

If we assume Jessica speaking the truth & she is not the culprit then other 3 must be liar. The truth that comes from Nicole's statement is that Sandy is telling truth. But only 1 is speaking truth not 2 as here Sandy & Jessica.

That means Jessica is lying. Which in turn means it was she who done that damage. Now Sandy's statement can't be true as we already have got culprit Jessica. 

Similarly, Mellisa lying as she is pointing towards Sandy.Two person not telling truth at a time as per provided information.

So only left with Nicole who is telling the truth that Sandy is liar.

Hence we can conclude that, Jessica knocked over the monitor & Nicole is telling the truth.

Who is Liar?

Suppose there are twin brothers; one which always tells the truth and one which always lies.  What single yes/no question could you ask to either brother to figure out which one is which? (Condition is you can't ask question whose answer you already know. e.g. does earth rotate around the sun?)

This should be that question! 

Source 

Question To Identify Liar/Truth Teller

First know about twins. 

We should ask one question,

"Would your brother say that you tell the truth?"

Now if the question is asked the truth teller, then he knows his liar brother would say NO to this question. Hence he would say NO straightaway.

And if the question being asked to liar then he knows that his brother is going to say NO to this question but as a liar he would lie once again & would say YES to the question asked.

So depending on what reply we get, we can easily identify the liar & truth teller brother.