The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin

Tricky question.

I got C (incorrect, 3 minutes) but I will still go ahead and post my explanation to see where I went wrong.

Per statement 1, (x*y)+y=1 ---> treat (x*y) as 'z' for now ---> z+y=1

Based on the table, a+b = 1 for 3 cases:

a=0,b=1 ---> z=0,y=1 ---> x*y=0 and y =1 ---> x=0 and y =1 ...(1)
a=1,b=0 ---> z=1,y=0 ---> x*y=1 and y =0 ---> Not possible per the table.
a=1,b=1 ---> z=1,y=1 ---> x*y=1 and y =1 ---> x=1 and y =1 ...(2)

Thus 2 possible combinations of x,y possible ---->2 values of x*y possible ----> Statement 1 is not sufficient.

Per statement 2, (x*y)+x=1 ---> treat (x*y) as 'z' for now ---> z+x=1

Based on the table, a+b = 1 for 3 cases:

a=0,b=1 ---> z=0,x=1 ---> x*y=0 and x =1 ---> x=1 and y =0 ...(3)
a=1,b=0 ---> z=1,x=0 ---> x*y=1 and x =0 ---> Not possible per the table.
a=1,b=1 ---> z=1,x=1 ---> x*y=1 and x =1 ---> x=1 and y =1 ...(4)

Thus 2 possible combinations of x,y possible ----> 2 values of x*y possible -----> Statement 2 is not sufficient.

Combining 1 and 2 , we get that x=1 and y =1 ---> x*y = 1. We get 1 unique value of x*y and C is thus the correct answer (IMO!)