**Sets A, B, and C with Non-Empty Intersections**

To find sets A, B, and C such that A ∩ B, B ∩ C, and A ∩ C are non-empty sets while A ∩ B ∩ C = {}, we can consider the following example:

Let's consider the following sets:
- Set A: {1, 2}
- Set B: {2, 3}
- Set C: {3, 4}

By analyzing the elements in each set, we can determine the intersections between them.

**Intersections:**
1. A ∩ B: The intersection between sets A and B is {2}, as they both share the element 2.
2. B ∩ C: The intersection between sets B and C is {3}, as they both share the element 3.
3. A ∩ C: The intersection between sets A and C is {}, as they do not share any common elements.

Now, let's explain this example in detail.

**Explanation:**

1. Set A: {1, 2}
- Set A contains two elements: 1 and 2.

2. Set B: {2, 3}
- Set B contains two elements: 2 and 3.

3. Set C: {3, 4}
- Set C contains two elements: 3 and 4.

Now, let's analyze the intersections between these sets.

**Intersections:**

1. A ∩ B: The intersection between sets A and B is {2}.
- The intersection contains the element 2 because it is present in both sets A and B.

2. B ∩ C: The intersection between sets B and C is {3}.
- The intersection contains the element 3 because it is present in both sets B and C.

3. A ∩ C: The intersection between sets A and C is {}.
- The intersection is empty as sets A and C do not share any common elements.

Finally, the intersection of all three sets, A ∩ B ∩ C, is {} (empty set) as there is no element that is present in all three sets simultaneously.

By constructing sets A, B, and C with the described elements, we have satisfied the conditions of having non-empty intersections between A and B, B and C, as well as A and C, while also ensuring that the intersection of all three sets is empty.