Let U= { 1,2,3,4,5,6,7,8,9,10 } be the universal set and let A = {2,3,4,5,6} and B = { 3,5,7,8} be its subsets .
Find B'

Answer

To find the complement of the set B (denoted as B'), we need to follow these steps:

### Step 1: Identify the Universal Set and Set B
We are given the universal set \( U \) and the set \( B \):
- Universal Set \( U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \} \)
- Set \( B = \{ 3, 5, 7, 8 \} \)

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

### Step 3: List the Elements of Set B
From the information given, the elements of set \( B \) are:
- \( B = \{ 3, 5, 7, 8 \} \)

### Step 4: Identify Elements in U that are Not in B
Now, we will go through the universal set \( U \) and exclude the elements that are present in set \( B \):
- From \( U \), we check each element:
- \( 1 \) is not in \( B \)
- \( 2 \) is not in \( B \)
- \( 3 \) is in \( B \) (exclude it)
- \( 4 \) is not in \( B \)
- \( 5 \) is in \( B \) (exclude it)
- \( 6 \) is not in \( B \)
- \( 7 \) is in \( B \) (exclude it)
- \( 8 \) is in \( B \) (exclude it)
- \( 9 \) is not in \( B \)
- \( 10 \) is not in \( B \)

### Step 5: Compile the Elements of B'
After excluding the elements of \( B \) from \( U \), we are left with:
- \( B' = \{ 1, 2, 4, 6, 9, 10 \} \)

### Final Answer
Thus, the complement of set \( B \) is:
- \( B' = \{ 1, 2, 4, 6, 9, 10 \} \)

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