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: 
Assuming all four know who broke it, let's use symbols: $+$ (telling truth), $-$ (telling lie), $\times$ (broke), $o$ (did not break). Let's consider $a)$ case by case:
$$1) \ Kane \ + \ (Dave \ \times) \Rightarrow Rose \ o \ (Rose \ +) \ ? \ (2 \ +)$$
$$2) \ Dave \ + \ (Kane \ - \ ) \Rightarrow K \ - \ (Dave \ o \ ) \Rightarrow Ron \ - \ (K \ o\ ) \Rightarrow Rose \ - \ (Rose \ \times) \ !$$
$$3) \ Ron \ + \ (Kane \ - \ ) \Rightarrow Kane \ - \ (Dave \ o \ ) \Rightarrow Dave \ + \ (Kane \ - \ ) \ ? \ (2 \ +)$$
$$4) \ Rose \ + \ (Rose \ o \ ) \Rightarrow Ron \ - \ (Kane \ o \ ) \Rightarrow Kane \ - \ (Dave \ o \ ) \Rightarrow Dave \ + \ (Kane \ o \ ) \ ? \ (2 \ +)$$
Using symbols probably makes this harder rather than easier. Just try some things. If Kane broke it, then Kane is lying, but the others are telling the truth, so you have three true statements. Well, that's not what you are looking for. So, try something else.