If `A = {1,2,3,4} and B={5,6,7}` , then `A nn B` is :

Options

A. `{1,2,3}`
B. `{5,6,7}`
C. `[4]`
D. `phi`

Answer

To find the intersection of sets A and B, we follow these steps:

1. **Identify the Elements of Each Set**:
- Set A = {1, 2, 3, 4}
- Set B = {5, 6, 7}

2. **Understand the Definition of Intersection**:
- The intersection of two sets, denoted as A ∩ B, consists of all elements that are common to both sets.

3. **Compare the Elements of Both Sets**:
- Look at the elements in Set A: 1, 2, 3, 4.
- Look at the elements in Set B: 5, 6, 7.
- Check if any elements from Set A are present in Set B.

4. **Determine Common Elements**:
- There are no elements in Set A (1, 2, 3, 4) that are also in Set B (5, 6, 7).
- Therefore, there are no common elements between the two sets.

5. **Conclude the Result**:
- Since there are no common elements, the intersection A ∩ B is the empty set.
- The empty set is denoted by the symbol ∅ or can also be represented as {}.

Thus, the result is:
A ∩ B = ∅