Let `U={1,2,3,4,5,6,7,8,9}, B={2,4,6,8} andC={3,4,5,6}`Find `(B-C)'`.

Explanation

To solve the problem of finding \((B - C)'\), we will follow these steps:

### Step 1: Identify the Universal Set (U), Set B, and Set C
Given:
- Universal Set \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \)
- Set \( B = \{2, 4, 6, 8\} \)
- Set \( C = \{3, 4, 5, 6\} \)

### Step 2: Calculate \( B - C \)
To find \( B - C \), we need to identify the elements that are in set \( B \) but not in set \( C \).

- **Element 2**: In \( B \) but not in \( C \) → Include 2
- **Element 4**: In \( B \) and also in \( C \) → Exclude 4
- **Element 6**: In \( B \) and also in \( C \) → Exclude 6
- **Element 8**: In \( B \) but not in \( C \) → Include 8

Thus, we have:
\[ B - C = \{2, 8\} \]

### Step 3: Find the Complement of \( B - C \)
The complement of \( B - C \) (denoted as \((B - C)'\)) consists of the elements in the universal set \( U \) that are not in \( B - C \).

- Elements in \( U \): \( \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \)
- Elements in \( B - C \): \( \{2, 8\} \)

Now, we will list the elements of \( U \) that are not in \( B - C \):
- **Element 1**: In \( U \) but not in \( B - C \) → Include 1
- **Element 2**: In \( B - C \) → Exclude 2
- **Element 3**: In \( U \) but not in \( B - C \) → Include 3
- **Element 4**: In \( U \) but not in \( B - C \) → Include 4
- **Element 5**: In \( U \) but not in \( B - C \) → Include 5
- **Element 6**: In \( U \) but not in \( B - C \) → Include 6
- **Element 7**: In \( U \) but not in \( B - C \) → Include 7
- **Element 8**: In \( B - C \) → Exclude 8
- **Element 9**: In \( U \) but not in \( B - C \) → Include 9

Thus, the complement of \( B - C \) is:
\[ (B - C)' = \{1, 3, 4, 5, 6, 7, 9\} \]

### Final Answer
\[ (B - C)' = \{1, 3, 4, 5, 6, 7, 9\} \]