To draw a Venn diagram representing the given facts about where each president served before assuming the presidency, we can create three overlapping circles representing the three categories: vice-president, Senate, and cabinet post.
Let's start by labeling the circles:
- Circle A: Represents the vice-president.
- Circle B: Represents the Senate.
- Circle C: Represents the cabinet post.
Now let's fill in the information given:
- 14 presidents were vice-president, so we write the number 14 inside circle A.
- 6 presidents served in the Senate, so we write the number 6 inside circle B.
- 15 presidents held a cabinet post, so we write the number 15 inside circle C.
We also have information about the overlap between these categories:
- 2 presidents were both vice-president and served in the Senate, so we write the number 2 in the overlapping region between circles A and B.
- 8 presidents were both vice-president and held a cabinet post, so we write the number 8 in the overlapping region between circles A and C.
- 4 presidents served in the Senate and held a cabinet post, so we write the number 4 in the overlapping region between circles B and C.
Finally, we know that 1 president was vice-president, served in the Senate, and held a cabinet post, so we write the number 1 in the region where all three circles overlap.
The completed Venn diagram should have the following numbers:
```
A: VP 14
_____._______________
C: Cabinet | 15
|
B: Senate 6
```
The number we are interested in is the one that represents the presidents who served as vice-president and in the Senate, but did not serve in a cabinet post. To find this number, we add up the numbers in the overlapping region between circles A and B (2 presidents) and subtract the number in the region where all three circles overlap (1 president).
Therefore, the number of presidents who served as vice-president and in the Senate but did not serve in a cabinet post is 2 - 1 = 1.