D = {0,1,-1,2,-2,3,-3,4,-4,...}
E = {1,2,4,9,16,25,36,49,64,81}
F = {12,14,16,18}
Finding an intersection of sets means listing the elements that are in both sets.
Finding a union of sets means listing all elements that are in either set.
With that in mind,
1. D intersect E = E because every element of E is a whole number, so it is in D also.
2. D intersect F = F because every element of F is a whole number, so it is in D also.
3. D intersect (E intersect F) First we find E intersect F = {16} because only 16 appears in E and F. Then, since 16 is also in D, D intersect (E intersect F) = {16}
4. We've already established that D contains everything in E and F. So when we take a union of (E intersect F) with D, we get all of D.
5. E union F = {1,4,9,12,14,16,18,25,36,49,64,81} because these are all the elements that are in either E or F. Intersecting with D doesn't change this list, since all are whole numbers.
