This is a good example of gemoro.
One has to first work out all the possibilities and then see if they fit in.
We have here two sets of people. Rav's father and mother and his father father who was R Chiyas father and his mothers mother who was R Chiyas mother.
We know one pair were dead and perhaps the other pair were alive but we dont which. It is possible that his parents were dead and his grandparents still alive.
We know it has to be a man and his wife who were dead.
There are two pshotim in the gemoro. Tosfos that Rav was telling the truth and Rashi that he wasnt. (Although rashi puts it differently)
So if rav was telling the truth. There are two possibilities.
1 If Rav chiya asked about the grandfather (his father) and rav answered truthfully that someone was alive. This could only be either his own mother like our girsa or his own father like the girsa brought in tosfos.
When Rav chiya asked again it could only have been about the grandmother since he was asking about the wife of the previous person and Ravs truthful answer could only have been about his own father like in our girsa or in tosfos girsa his own mother.
2 If Rav chiya asked about the father (his half brother), Rav's truthful reply could either be his grandmother was still alive like our girsa or his grandfather like tosfos girsa.
When Rav Chiya asked again it could only have been about his half sister, Rav's mother since he was asking about the wife of the previous person and Ravs truthful reply could only have been about his grandfather in our girsa or his grandmother like tosfo girsa.
3 Rashi says he did not answer truthfully.
So he asked the father and he replied the mother was still alive. Then he asked about the mother and he replied the father was still alive.
So all in all we have 5 pshotim in the gemoro. The first two contain two each.
The reason there are so many, is because of the many 'girsas' different versions of the gemoro.
The problems in the gemoro are why it had to start off telling us about Rav's exact relationship with R Chiya. Why Rav called his father by name. Why if R Chiya was asking about his half sister, Rav's mother, he should have used the wording 'your mother' not just plain 'mother' unless that was her name. Why if R Chiya asked about his own father the grandfather, why couldnt rav answer about his father R Chiyas brother that he was alive, why did he have to go to his mother in our girsa.