If U= {1,2,3,4,5,6,7,8,9,10} and A= {3,4,7,9}, then B equals :

Options

A. {1,2,8,10}
B. {1,2,5,8,10}
C. {1,2,5,6,8,10}
D. None of these.

Answer

To find the set B given the universal set U and the set A, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Universal Set (U)**:
The universal set U is given as:
\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \]

2. **Identify the Set A**:
The set A is given as:
\[ A = \{3, 4, 7, 9\} \]

3. **Determine Set B**:
To find set B, we need to subtract the elements of set A from the universal set U. This means we will take all elements in U that are not in A.

\[ B = U - A \]

4. **Perform the Subtraction**:
We will list the elements of U and remove the elements that are in A (3, 4, 7, 9):
- Start with U: \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
- Remove 3: Remaining elements are \{1, 2, 4, 5, 6, 7, 8, 9, 10\}
- Remove 4: Remaining elements are \{1, 2, 5, 6, 7, 8, 9, 10\}
- Remove 7: Remaining elements are \{1, 2, 5, 6, 8, 9, 10\}
- Remove 9: Remaining elements are \{1, 2, 5, 6, 8, 10\}

Thus, the elements left in set B are:
\[ B = \{1, 2, 5, 6, 8, 10\} \]

5. **Final Result**:
Therefore, the set B is:
\[ B = \{1, 2, 5, 6, 8, 10\} \]