Question

Which of the following is not equivalent to x - y + z?

z - y + x
x + z - y
y - x + z
z + x - y

Answer 1

y - x + z

Reason: x - y + z = x + z - y (commuting terms), and z - y + x and z + x - y are the same after reordering. But y - x + z = z + y - x, which is not equal to x - y + z in general (e.g. x=2,y=1,z=0 gives 1 vs -1).