Give the numbers of elements in the regions marked I, II, III, IV, V, VI, VII, VIII in the figure.


|U| = 240, |A| = 15, |B| = 14, |C| = 24 |A�¿B| = 4, |A�¿C| = 2, |B�¿C| = 7, |A�¿B�¿C| = 1
| I | = 1
| II | = 2
| III | = 3
| IV | = 4
| V | = 5
| VI | = 6
| VII | = 7
| VIII | = 8

If you look at the related questions below, there are now 5 of your questions. Since we can't see your figure, we have no idea what your are talking about.

To determine the numbers of elements in each region marked I, II, III, IV, V, VI, VII, VIII, we need to use the principle of inclusion-exclusion.

Let's break it down step by step:

1. We know the total number of elements in the universal set (U) is 240.

|U| = 240

2. We have the numbers of elements in individual sets A, B, and C.

|A| = 15
|B| = 14
|C| = 24

3. We are given the numbers of elements in the intersections of these sets.

|A∩B| = 4
|A∩C| = 2
|B∩C| = 7

4. We are also given the number of elements in the intersection of all three sets.

|A∩B∩C| = 1

Now, we can calculate the numbers of elements in each region:

| I | = |A∩B∩C| = 1 (This region represents the intersection of all three sets)

| II | = |A∩B| - |A∩B∩C| = 4 - 1 = 3 (This region represents the intersection of sets A and B, excluding the intersection with set C)

| III | = |B∩C| - |A∩B∩C| = 7 - 1 = 6 (This region represents the intersection of sets B and C, excluding the intersection with set A)

| IV | = |A∩C| - |A∩B∩C| = 2 - 1 = 1 (This region represents the intersection of sets A and C, excluding the intersection with set B)

| V | = |A| - |A∩B| - |A∩C| + |A∩B∩C| = 15 - 4 - 2 + 1 = 10
(This region represents the elements in set A that are not in the intersections with sets B and C)

| VI | = |B| - |A∩B| - |B∩C| + |A∩B∩C| = 14 - 4 - 7 + 1 = 4
(This region represents the elements in set B that are not in the intersections with sets A and C)

| VII | = |C| - |A∩C| - |B∩C| + |A∩B∩C| = 24 - 2 - 7 + 1 = 16
(This region represents the elements in set C that are not in the intersections with sets A and B)

| VIII | = |U| - |A| - |B| - |C| + |A∩B| + |A∩C| + |B∩C| - |A∩B∩C| = 240 - 15 - 14 - 24 + 4 + 2 + 7 - 1 = 189
(This region represents the elements that do not belong to any of the sets A, B, or C)

Therefore, the numbers of elements in the regions marked I, II, III, IV, V, VI, VII, VIII are:
| I | = 1
| II | = 3
| III | = 6
| IV | = 1
| V | = 10
| VI | = 4
| VII | = 16
| VIII | = 189