let U= {1,2,3,4,5,6,7,8} A = {1,2,,3,4} then find the A complement

Explanation

To find the complement of the set A with respect to the universal set U, we will follow these steps:

### Step 1: Identify the Universal Set and Set A
The universal set \( U \) is given as:
\[ U = \{1, 2, 3, 4, 5, 6, 7, 8\} \]

The set \( A \) is given as:
\[ A = \{1, 2, 3, 4\} \]

### Step 2: Understand the Concept of Complement
The complement of a set \( A \) (denoted as \( A' \) or \( A^c \)) consists of all the elements in the universal set \( U \) that are not in set \( A \).

### Step 3: List the Elements of Set A
From the information provided, the elements in set \( A \) are:
\[ A = \{1, 2, 3, 4\} \]

### Step 4: Identify Elements in the Universal Set that are not in A
Now, we will find the elements in the universal set \( U \) that are not included in set \( A \):
- The elements in \( U \) are: \( 1, 2, 3, 4, 5, 6, 7, 8 \)
- The elements in \( A \) are: \( 1, 2, 3, 4 \)

Now, we will exclude the elements of \( A \) from \( U \):
- Remaining elements in \( U \) that are not in \( A \): \( 5, 6, 7, 8 \)

### Step 5: Write the Complement of Set A
Thus, the complement of set \( A \) is:
\[ A' = \{5, 6, 7, 8\} \]

### Final Answer
The complement of set \( A \) is:
\[ A' = \{5, 6, 7, 8\} \]

---