You may want to review intervals first.
There are two operations you can do on intervals. One is intersect. This is written ‘∩’. This means you want only the points in both intervals. So the new lower bound will be the bigger of the two lower bounds, and the new upper bound will be the smaller of the two upper bounds. The idea is that we want to make them as strict as we can.
The other operation is called union. This is written ‘∪’. This means you want all the points in either interval. So we don't want to make the bounds strict at all. Therefore, the new lower bound will be the smaller of the two lower bounds, and the new upper bound will be the bigger of the two upper bounds.
Remember that ∞ and −∞ mean there's no bound at all. That's not strict at all! So, if we want to compute (−∞, 2) ∩ [−1, 2), the stricter lower bound is −1. Since both upper bounds are 2, the answer is [−1, 2). Note that we put a bracket on the left in the answer, because in the question there was a bracket with −1. Since there was a parenthesis with 2, we put a parenthesis next to 2 in the answer too. If we had been asked for (−∞, 2) ∪ [−1, 2), then we would have wanted to use the less strict lower bound, so we would have written (−∞, 2). We put a parenthesis next to −∞ because we had one in the question.