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

Options

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

Answer

To solve the problem of finding the intersection of two sets A and B, we follow these steps:

### Step 1: Identify the Sets
We have two sets:
- Set A = {1, 2, 3, 4}
- Set B = {5, 6, 7}

### Step 2: Understand the Concept of Intersection
The intersection of two sets, denoted as \( A \cap B \), is the set of elements that are common to both sets.

### Step 3: Compare the Elements of Both Sets
Now, we will look for elements that are present in both Set A and Set B:
- Elements in Set A: 1, 2, 3, 4
- Elements in Set B: 5, 6, 7

### Step 4: Identify Common Elements
We check each element in Set A to see if it is also in Set B:
- 1 is not in B
- 2 is not in B
- 3 is not in B
- 4 is not in B

Since none of the elements in Set A are present in Set B, there are no common elements.

### Step 5: Conclusion
Since there are no common elements between Set A and Set B, the intersection \( A \cap B \) is an empty set.

### Step 6: Denote the Empty Set
The empty set is denoted by the symbol \( \emptyset \) or sometimes by the symbol \( \phi \).

Thus, the final answer is:
\[ A \cap B = \emptyset \text{ or } \phi \]

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