Part (a)
The notation
talks about overlapping or intersecting all three intervals. Your teacher wants to know what numbers are in all three intervals at the same time.
Refer to the diagram below. I've graphed regions A, B and C on the same number line. The vertical separation is to help tell the regions apart. Technically they should all be on the same number line. Notice how the regions overlap on the interval (0, 2] which translates over to
telling us that the answer must be choice D.
Meaning we exclude 0 but keep 2, and everything in between the endpoints.
Choice C is not possible because x = -1 is not in region C. This means choice A is ruled out also. Choice B is eliminated because x = 3 is not in region A nor region B.
Answer: Choice D
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Part (b)
As mentioned earlier, the intervals all have in common the region between x = 0 and x = 2. We exclude 0 but keep 2.
Answer: (0, 2]
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Part (c)
The graph is shown below.
We have an open circle at 0 and a closed circle at 2. There is shading in between those endpoints.
When it comes to graphing the final answer, you'll ignore the separate regions A,B,C and only graph what is shown in purple.