Question

Please help!!

Answer 1

Answer: $(28, 91) \cup (93, 94)$

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Explanation:

Check out the diagram below.

I have drawn out two number lines with the key points 28,91,93,94 marked on them. The diagram isn't to scale, but that doesn't matter. All that matters is that the numbers line up (eg: we have the two 28's line up vertically).

The first number line drawing on top shows the shading for set A. Everything in the shaded region is either smaller than 91, or larger than 93, or 93 itself. We exclude 91 due to the curved parenthesis. The square bracket says to include the 93.

For the second graph, you have two endpoints as open holes (to exclude both endpoints) and you shade everything between.

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After you draw the two number line regions, you would then mark off the interval(s) that they share in common.

The notation $A \cap B$ means "A intersect B" which means we want to find the stuff that is in both sets at the same time.

So we'll have two pieces here. The portion from 28 to 91 is the first interval, and then the second portion runs from 93 to 94. For each interval sub-piece, the endpoints are excluded

So that leads to the final answer $(28, 91) \cup (93, 94)$