At the time of George W.Bush's presidency, there have been 43 presidents of the United States. Draw a Venn diagram showing the following facts about where each served before assuming the presidency. How many presidents served as vice-president and in the Senate, but did not serve in a cabinet post?
14 were vice-president.
6 served in the Senate.
15 held a cabinet post.
2 were VP and served in the Senate.
8 were VP and a held a cabinet post.
4 served in the Senate and held a cabinet post.
1 was VP, in the Senate, and held a cabinet post.
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.
To draw the Venn diagram, we need to consider the following information:
- 14 presidents served as vice-president
- 6 presidents served in the Senate
- 15 presidents held a cabinet post
- 2 presidents were vice-president and served in the Senate
- 8 presidents were vice-president and held a cabinet post
- 4 presidents served in the Senate and held a cabinet post
- 1 president was vice-president, in the Senate, and held a cabinet post
Let's break down the information step by step:
Step 1: Draw three overlapping circles to represent the categories: vice-president, Senate, and cabinet.
Step 2: Label each circle accordingly: VP, Senate, and Cabinet.
Step 3: Place the number 14 inside the VP circle to represent the 14 presidents who served as vice-president.
Step 4: Place the number 6 inside the Senate circle to represent the 6 presidents who served in the Senate.
Step 5: Place the number 15 inside the Cabinet circle to represent the 15 presidents who held a cabinet post.
Step 6: Since 2 presidents served as vice-president and in the Senate, place the number 2 in the overlapping area of the VP and Senate circles.
Step 7: Since 8 presidents were vice-president and held a cabinet post, place the number 8 in the overlapping area of the VP and Cabinet circles.
Step 8: Since 4 presidents served in the Senate and held a cabinet post, place the number 4 in the overlapping area of the Senate and Cabinet circles.
Step 9: Since 1 president was vice-president, in the Senate, and held a cabinet post, place the number 1 in the intersection area of all three circles.
The final Venn diagram should show the distribution of presidents in each category, as described above.
___
| |
| VP |
|___|
___
| |
| S |
|___|
___
| |
| C |
|___|
VP: 14
S: 6
C: 15
VP & S: 2
VP & C: 8
S & C: 4
VP & S & C: 1
Now, to answer the specific question, we need to find the number of presidents who served as vice-president and in the Senate, but did not serve in a cabinet post. This number can be found by subtracting the number of presidents in the overlapping area of VP, S, and C (1) from the number of presidents in the overlapping area of VP and S (2).
Therefore, 2 - 1 = 1 president served as vice-president and in the Senate, but did not serve in a cabinet post.