Which of the following sets are disjoint ?
`A = {2,3},B={4,5,6}`
`C = {3,5,8},D={1,5,7}`.

Answer

To determine which of the given sets are disjoint, we need to check the intersections of the sets. Disjoint sets are defined as sets that have no elements in common. Let's analyze the sets step by step.

### Step 1: Identify the Sets
We have the following sets:
- \( A = \{2, 3\} \)
- \( B = \{4, 5, 6\} \)
- \( C = \{3, 5, 8\} \)
- \( D = \{1, 5, 7\} \)

### Step 2: Check A and B
To check if sets \( A \) and \( B \) are disjoint, we find their intersection:
\[ A \cap B = \{2, 3\} \cap \{4, 5, 6\} = \emptyset \]
Since the intersection is empty, sets \( A \) and \( B \) are disjoint.

### Step 3: Check A and C
Now, we check sets \( A \) and \( C \):
\[ A \cap C = \{2, 3\} \cap \{3, 5, 8\} = \{3\} \]
Since the intersection is not empty, sets \( A \) and \( C \) are not disjoint.

### Step 4: Check A and D
Next, we check sets \( A \) and \( D \):
\[ A \cap D = \{2, 3\} \cap \{1, 5, 7\} = \emptyset \]
Since the intersection is empty, sets \( A \) and \( D \) are disjoint.

### Step 5: Check B and C
Now, we check sets \( B \) and \( C \):
\[ B \cap C = \{4, 5, 6\} \cap \{3, 5, 8\} = \{5\} \]
Since the intersection is not empty, sets \( B \) and \( C \) are not disjoint.

### Step 6: Check B and D
Next, we check sets \( B \) and \( D \):
\[ B \cap D = \{4, 5, 6\} \cap \{1, 5, 7\} = \{5\} \]
Since the intersection is not empty, sets \( B \) and \( D \) are not disjoint.

### Step 7: Check C and D
Finally, we check sets \( C \) and \( D \):
\[ C \cap D = \{3, 5, 8\} \cap \{1, 5, 7\} = \{5\} \]
Since the intersection is not empty, sets \( C \) and \( D \) are not disjoint.

### Summary of Results
The disjoint sets are:
- \( A \) and \( B \)
- \( A \) and \( D \)

### Final Answer
The disjoint sets are \( A \) and \( B \), and \( A \) and \( D \).

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