We can Imagine drawing number lines (Venn diagrams in more complex examples) as such:
( -∞ --------------------------- -66 ] U [ 80 ----------------------------- +∞ ) Set A
( -74 ---------------------------- 89 ) Set B
When we use the ∩ symbol, we want the intersect of the two sets. This means all the elements that are in A and B. For our simple diagram his means putting bounds on where our lines overlap.
From the diagram we can see that -74 is included in Set A but not in Set B. Wen can then see that every number between -74 and -66 is in both Set A and Set B. It is important to remember that "]" means it is included in the set (Set A for our example).
This means our answer so far is ( -74, -66]. Now lets look a little further down the number line. Everything in between (not including) -66 and 80 is in Set B, but not in Set A, so we don't want that. Now we see that 80 is included in both Sets A and B, as well as everything up until 89 which is not in Set B, but is in Set A. This means we want all numbers from 80 (including 80) until 89 (not including 89).
That will look like: [80, 89).
So now we have two separate sets that meet the requirements set forth by the question. This means that the complete answer includes both of those joined together, and the way we do that is with a "union" written as ∪.
This gives us the complete answer:
A ∩ B = ( -74, -66] ∪ [80, 89)
