For each of the following, draw a Venn diagram.
(a) A �º B, C �º B, A �¿ C = ∅
(b) A �» C, B �¿ C = ∅.
To draw a Venn diagram, we need to understand the relationships between the given sets. Let's break down each scenario and create the corresponding Venn diagram:
(a) A �º B, C �º B, A �¿ C = ∅
In this case, we have three sets: A, B, and C.
1. A �º B: This means that set A is completely contained within set B. We represent this by drawing a circle for set B and placing another smaller circle entirely inside it to represent set A. The overlap between A and B is the entire circle of A.
2. C �º B: This tells us that set C is also entirely contained within set B. We represent this by drawing another circle for set C inside the circle of set B. The overlap between C and B is the entire circle of C.
3. A �¿ C = ∅: This means there is no overlap between sets A and C. We represent this by ensuring that the circles for A and C do not intersect or overlap.
Combining all of these conditions, the Venn diagram would look like this:
```
_______ _______
| | | |
| A | | C |
| | | |
‾‾‾‾‾‾‾ ‾‾‾‾‾‾‾
| |
| B |
|_________|
```
(b) A �» C, B �¿ C = ∅
Again, we have three sets: A, B, and C.
1. A �» C: This means that there is a subset relationship between A and C, where A is a superset of C. In other words, every element in set C is also in set A. We represent this by drawing a circle for set A and placing another circle inside it that represents set C. The overlap between A and C is the entire circle of C.
2. B �¿ C = ∅: This implies that there is no overlap between sets B and C. We represent this by ensuring that the circles for B and C do not intersect or overlap.
Combining these conditions, the Venn diagram would look like this:
```
_______ _______
| | | |
| C | | B |
| | | |
‾‾‾‾‾‾‾ ‾‾‾‾‾‾‾
| |
| A |
|_________|
```
Note that the circles representing the sets are not necessarily drawn to scale and their relative sizes may vary depending on the specific elements in each set.