Answer:
To construct Euler circles for the sets E, K, and M, we need to understand the relationships between these sets. Let's analyze the given information:
E is the set of two-story houses in the city.
K is the set of five-story houses in the city.
M is the set of houses in the city.
Based on this information, we can infer that E and K are subsets of M. In other words, all two-story houses (E) and five-story houses (K) are included in the set of all houses (M). However, it is important to note that not all houses in M are necessarily two-story or five-story houses.
Now, let's construct Euler circles to visually represent these relationships:
Euler circle for E:
```
_______
| |
| E |
|_______|
```
This circle represents the set E, which consists of two-story houses.
Euler circle for K:
```
_______
| |
| K |
|_______|
```
This circle represents the set K, which consists of five-story houses.
Euler circle for M:
```
_______
| |
| M |
|_______|
```
This circle represents the set M, which consists of all houses in the city.
Since E and K are subsets of M, we can represent this relationship by placing E and K circles inside the M circle:
```
_______
| |
| E |
|_______|
_______
| |
| K |
|_______|
_______
| |
| M |
|_______|
```
In this diagram, both E and K are completely contained within M, indicating that all two-story and five-story houses are part of the set of all houses.
Explanation: