In a survey of 200 families, the number

that read recent issues of a certain monthly
Journal were found to be - March only 36,
March but not April 46; March and
16 March Sai May 96: May and April
16. none of the 3 months 48. By means
of Venn diagram
or otherwise determine
is the number of families that read April issue
2) the number of families that read two
Consecutive issues?
3) the number of families that read the May
issue, if and only if they did not read
April issue?
4)the number of families that read March
and April issues but not the May issue​

Cannot diagram on these posts.

To solve this problem using a Venn diagram, we can start by drawing three overlapping circles to represent the months of March, April, and May. We can label the circles M, A, and S respectively, where M represents March, A represents April, and S represents May.

Next, let's fill in the given information:

- March only: 36 families (marked in circle M)
- March but not April: 46 families (marked in circle M)
- March and May: 96 families (marked in circles M and S)
- May and April: 16 families (marked in circles S and A)
- None of the 3 months: 48 families (outside of all circles)

Now, let's determine the remaining information:

1) To find the number of families that read the April issue, we need to find the overlapping area between circles A and M. From the given information, we know that 46 families read March but not April. Therefore, the number of families that read the April issue is: 46 + 16 = 62.

2) To find the number of families that read two consecutive issues, we need to find the overlapping area between circles A and S, as well as the overlapping area between circles M and A. From the given information, we know that 16 families read May and April. Therefore, the number of families that read two consecutive issues is: 16 + 62 = 78.

3) To find the number of families that read the May issue, but not the April issue, we need to find the area within the circle S but outside of circle A. Since 16 families read both May and April, we subtract this number from the total number of families that read May (which is given as 96). Therefore, the number of families that read the May issue but not the April issue is: 96 - 16 = 80.

4) To find the number of families that read March and April, but not the May issue, we need to find the overlapping area between circles M and A, while excluding the overlapping area with circle S. From the given information, we know that 46 families read March but not April. Therefore, the number of families that read March and April, but not May, is: 46 - 16 = 30.

So, the answers to the questions are:
1) The number of families that read the April issue is 62.
2) The number of families that read two consecutive issues is 78.
3) The number of families that read the May issue, if and only if they did not read the April issue, is 80.
4) The number of families that read March and April issues but not the May issue is 30.

To solve this problem, we will use a Venn diagram to represent the various overlapping categories of families that read the different issues of the monthly journal.

Let's start by drawing three circles to represent the three months: March, April, and May. The size of each circle corresponds to the number of families that read that particular issue.

1) To find the number of families that read the April issue, we need to determine the total number of families within the April circle. We know that the total number of families surveyed is 200, and the number of families that read March and April is 46. However, this includes the families that also read May, so we need to subtract that.

Using the formula for a set intersection, we can calculate the number of families that read both March and April, but not May:
March and April only = March and April - March and April and May
March and April only = (46) - (16)
March and April only = 30

Thus, the number of families that read the April issue is 30.

2) To find the number of families that read two consecutive issues, we need to find the total number of families within the overlapping region between the three circles. This region represents the families that read both March and April, both April and May, or both May and March.

Using the formula for the union of sets, we can calculate the number of families in this region:
Total families that read two consecutive issues = March and April only + April and May + May and March - (March only + April only + May only)

Plugging in the given values and values we have already determined:
Total families that read two consecutive issues = (30) + (16) + (96) - (36 + 30 + 16)
Total families that read two consecutive issues = 62

Therefore, the number of families that read two consecutive issues is 62.

3) To find the number of families that read the May issue if and only if they did not read the April issue, we need to find the overlap between the May circle and the complement of the April circle (the region outside the April circle).

Using the formula for the set complement, we can calculate the number of families in this region:
May only (excluding April) = May - April and May
May only = (16) - (16)
May only = 0

Therefore, there are no families that read the May issue if they did not read the April issue.

4) To find the number of families that read both the March and April issues but not the May issue, we need to find the overlap between the March and April circles, excluding the overlap with the May circle.

Using the formula for set intersection and set complement, we can calculate the number of families in this region:
March and April only (excluding May) = March and April - March and April and May
March and April only = (46) - (16)
March and April only = 30

Therefore, the number of families that read both the March and April issues but not the May issue is 30.

In summary:
1) The number of families that read the April issue is 30.
2) The number of families that read two consecutive issues is 62.
3) There are no families that read the May issue if they did not read the April issue.
4) The number of families that read both the March and April issues but not the May issue is 30.