Asifpirlo
The possible arguments of the functions f(x,y) and g(x,y) are x=0 or 1 and y = 0 or 1 and are defined by the following tables (Attachment):

What is the value of f(a,b) + g(a,b) ?
(1) f(a,b) = 0
(2) g(a,b)= 0

Yellow rows are the values of x, green columns are the values of y, and the red boxes are the outcomes of the functions f and g.
The possible arguments of the functions f(x,y) and g(x,y) are x=0 or 1 and y = 0 or 1 and are defined by the following tables:
What is the value of f(a,b) + g(a,b) ?(1) f(a,b) = 0. According to the second table we can have the following cases:
a=0, b=0 --> f(a,b) + g(a,b) = 0 + 0 = 0;
a=1, b=0 --> f(a,b) + g(a,b) = 0 + 1 = 1;
a=0, b=1 --> f(a,b) + g(a,b) = 0 + 1 = 1.
Not sufficient.
(2) g(a,b) = 0. According to the first table we can have only the following case:
a=0, b=0 --> f(a,b) + g(a,b) = 0 + 0 = 0.
Sufficient.
Answer: B.
Hope it's clear.
hi bunuel , can't a=1 and b=1 also be a possible domain for f(a,b) as you have mentioned only 3 possible cases