Are sets `A={1,2,3,4,},B={X: X in N and 5 le x le 7}` disjoint ?Justify?

Answer

To determine if the sets \( A \) and \( B \) are disjoint, we need to analyze the elements of both sets and check if they share any common elements.

### Step-by-Step Solution:

1. **Identify the elements of Set A:**
\[ A = \{1, 2, 3, 4\} \]

2. **Define Set B:**
Set \( B \) is defined as:
\[ B = \{ x : x \in \mathbb{N} \text{ and } 5 \leq x \leq 7 \} \]
This means \( B \) includes natural numbers \( x \) that are greater than or equal to 5 and less than or equal to 7.

3. **List the elements of Set B:**
The natural numbers in the range from 5 to 7 are:
\[ B = \{5, 6, 7\} \]

4. **Check for common elements:**
Now, we need to check if there are any common elements between sets \( A \) and \( B \).
- Elements of \( A \): \( 1, 2, 3, 4 \)
- Elements of \( B \): \( 5, 6, 7 \)

5. **Determine the intersection of Sets A and B:**
The intersection \( A \cap B \) is the set of elements that are in both \( A \) and \( B \). Since:
\[ A \cap B = \{ \} \quad (\text{no common elements}) \]

6. **Conclusion:**
Since the intersection of sets \( A \) and \( B \) is empty, we conclude that the sets are disjoint.

### Final Answer:
Sets \( A \) and \( B \) are disjoint because they have no elements in common.

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