If U= {1,2,3,4,..,10} and A= {1,2,3,4}. Then, `(A')` is equal to

Options

A. A
B. U
C. `phi`
D. None of these

Answer

To find the complement of set A (denoted as A'), we will 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:
\[ A = \{1, 2, 3, 4\} \]

3. **Determine the Complement of A (A')**:
The complement of A, denoted as A', consists of all the elements in the universal set U that are not in set A. To find A', we will subtract the elements of A from U:
\[ A' = U - A \]

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

5. **Write the Final Answer**:
Therefore, the complement of A is:
\[ A' = \{5, 6, 7, 8, 9, 10\} \]

### Final Answer:
\[ A' = \{5, 6, 7, 8, 9, 10\} \]