Question: One of Kane, Dave, Ron or Rose broke a vase. The following is what each of them had to tell about the person who broke the vase:

1. Kane: Dave broke it.
2. Dave: Kane lied.
3. Ron: Kane broke it.
4. Rose: I did not break it.

(a) If only one of these statements is true who broke the vase? 

(b) If only two of these statements are true who broke the vase? Justify your answer.

I tried to answer this by taking ,

Let p = Kane broke the vase , q = Dave broke the vase , r = Ron broke the vase and s = Rose broke the vase. 

So the statements Dave broke it = q , Kane lied = -q , Kane broke it = p and I did not break it (Rose) = s 

Both q and q cannot be either true or false simultaneously. 

Then how to proceed ? I'm stuck here

Answer: 
This problem can be more easily visualized/solved by making a table:

[![enter image description here](https://i.stack.imgur.com/5kM34.jpg)](https://i.stack.imgur.com/5kM34.jpg)

Assuming the person in the left column broke the vase, we can conclude which statements are true or false.
It is important to notice that this arrangement only works if it is assumed that every other character knows who broke the vase.

Both Parts A and B are now Trivial:

A) Rose must have broken the vase, as that is the only way in which only one person (Dave) has told the truth.

B) There are two solutions:

-1) Dave broke the vase, Kane and Rose are telling the truth.

-2) Ron broke the vase, Dave and Rose are telling the truth.
Changing the names of protagonists, it becomes obvious who broke the vase in situation **(b)**.

$\begin{array}{l}
\text{Clovis :} & \text{The soldier broke it}\\
\text{Soldier :} & \text{Clovis lied}\\
\text{Gregoire :} & \text{Clovis broke it}\\
\text{St Remi :} & \text{I did not broke it}\\
\end{array}$

:-)