Match the following.

Given

D = x is a whole number

E = x

F = x is an even number between 10 and 20

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.