Option (A) :It is lossless but not dependency preserving lossless.
Explaination :-
Dependency preserving: Even if there are many functional dependencies in Relation R, all of them won't be applicable, Only functional dependencies which contain only these attributes:-
{ABC} AB->C , AC->B , BC-> A
{ACDE} AD->E
{ADG} AD->G
The lost functional dependencies are B->D and E->G, They cannot be derived even when the table is joined.
lossless:-
There are two types lossy decomposition(when extra tuples are added when the tables are re-joined) and lossless decomposition(no extra tuples gets added, Original tuples are reformed)
The condition for lossless join is : If the common attribute is the key in one of the tables.
Between table {ABC and ACDE} AC is key of table {ABC} and hence between table {ACDE} and {ADC}, AD is common and key attribute of table {ADG and ACDE}
Hence, the table is lossless.