Question

Select the statements that are true based on the following given information.
D = {x | x is a whole number}
E = {x | x is a perfect square < 36}
F = {x | x is an even number between 20 and 30}

The expression D ∩ E is {1, 4, 9, 16}.
The expression D ∩ F is {12, 14, 16, 18}.
D ∪ (E ∩ F) is {all whole numbers}.
(E ∩ F) is the empty set.
The expression D ∩ (E ∪ F) is 25

Answer 1

D={all real whole numbers}
E={4,9,16,25}
F={22,24,26,28}

FALSE__the expression D∪E = E.
"D∪E = E" is false because D∪E includes all real whole numbers and E only includes {4,9,16,25}
FALSE__E∪(D∩F) is {25}.
{4,9,16,25}∪{22,24,26,28}={4,9,16,22,2... not just {25}
TRUE__F⊂D
{22,24,26,28} is a subset of {all real whole numbers}
TRUE__(E∩F) is the empty set.
{4,9,16,25}∩{22,24,26,28} = { }
FALSE__Set E is infinite.
{4,9,16,25} is not infinite

Answer 2

Match the following.

Given

D = {x | x is a whole number}
E = {x | x is a perfect square < 100}
F = {x | x is an even number between 10 and 20}

1. D ∩ E {all whole numbers}
2. D ∩ F {12, 14, 16, 18}
3. D ∩ (E ∩ F) {1, 4, 9, 16, 25, 36, 49, 64, 81}
4. D ∪ (E ∩ F) {1, 4, 9, 16, 25, 36, 49, 64, 81, 12, 14, 18}
5. D ∩ (E ∪ F) {16}

Answer 3

@Agl202

Answer 4

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.