To determine which choice is NOT equal to the others, we need to understand how the brackets are being used in the options provided. It appears that the brackets represent the floor function, denoted by \(\lfloor x \rfloor\), which returns the largest integer less than or equal to \(x\).
Now let's evaluate each option:
- A: \(-\left[\frac{2}{5}\right]\)
- B: \(\left[-\frac{2}{5}\right]\)
- C: \(\left[\frac{2}{5}\right]\)
- D: \(\left[\frac{2}{-5}\right]\)
Let's calculate each one:
-
Calculate \(\frac{2}{5} = 0.4\):
- \(\left[\frac{2}{5}\right] = \lfloor 0.4 \rfloor = 0\)
-
Calculate \(-\left[\frac{2}{5}\right]\):
- \(-\left[\frac{2}{5}\right] = -0 = 0\)
-
Calculate \(-\frac{2}{5} = -0.4\):
- \(\left[-\frac{2}{5}\right] = \lfloor -0.4 \rfloor = -1\)
-
Calculate \(\frac{2}{-5} = -0.4\):
- \(\left[\frac{2}{-5}\right] = \lfloor -0.4 \rfloor = -1\)
Now we summarize the values:
- A = 0
- B = -1
- C = 0
- D = -1
From this breakdown:
- A and C both equal 0.
- B and D both equal -1.
Thus, the choice that is NOT equal to the others is B: \(\left[-\frac{2}{5}\right]\), as it equals -1, while the others equal 0.
So the answer is B.