As every choice has an OR, both conditions must be true. Let's check:

a)x=-1 OR y=0:
x=-1:
0*y = y --> false, as y may be any value (e.g. 5)
This also excludes choice d)

b)x=0 OR y=0:
x=0:
1*y = y --> true, let's proceed to the second condition
y=0:
0*(1+x)=0 --> true, regardless x's value

So, the correct answer is B

If we checked the remaining choices:
C) x=1 --> 2*y = y (cannot be true)
D) already excluded
E) y=1 --> x+1 = 1 --> false as x can hold any value (e.g. 5)

Max@Math Revolution wrote:If (1+x)y=y, which of the following must be true?
A. x=-1 or y=0
B. x=0 or y=0
C. x=1 or y=1
D. x=-1 or y=-1
E. x=0 or y=1

*An answer will be posted in 2 days.

Answer is B. If x = 0, the equation simplifies to y = y, which is true for all values of y. If y = 0, the equation simplifies to 0(1-x) = 0, which is true for all values of x.

From y+xy=y, we get xy=0. Hence, the correct answer is B.