@Neha singh. Remember one thing(rather thumb rule). If you know the concept (and not the shortcut),its okay. Just take an example an compute it. GATE exam setters put the question in such a way that it can be computed in max 2 min even with basic knowledge.SO, lets assume that I dont know the shortcut. Lets have an example.
Serial no(X) Name(Y) Lives at flat no(Z) owns car model name(W)
1 sush 520 Y
2 kim 521 Y ...............(kim and sush are wife and husband :) )
3 Arush 522 Z
---------------------------------------------------------------------------------------
Lets evaluate option (C).
R1
Serial no(X) owns car model name(W)
1 Y
2 Y
3 Z
----------------------------------------------------------
R2
Name(Y) owns car model name(W)
sush Y
kim Y
Arush Z
---------------------------------------------------------------
R3
Lives at flat no(Z) owns car model name(W)
520 Y
521 Y
522 Z
Now, even R1(natural join) R2 will yield 6 tuples (instead of 3 in the original for columns pertaining to R1 and R2).
So, R1(natural join) R2 (natural join) R3 will definitely yeild more tuples than 3.
Hence, lossy join decomposition.