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 A'

Answer

To find the complement of set A (denoted as A'), we need to identify the elements in the universal set U that are not in set A. Let's go through the steps systematically:

### Step 1: Identify the Universal Set and Set A
- The universal set U is given as:
\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \]
- Set A is given as:
\[ A = \{2, 3, 4, 5, 6\} \]

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

### Step 3: List the Elements of Set A
- The elements of set A are:
\[ A = \{2, 3, 4, 5, 6\} \]

### Step 4: Remove Elements of Set A from the Universal Set
- Now, we will remove the elements of set A from the universal set U:
- Start with U: \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
- Remove 2, 3, 4, 5, and 6 from U.

### Step 5: Identify the Remaining Elements
- After removing the elements of A from U, we are left with:
\[ A' = \{1, 7, 8, 9, 10\} \]

### Final Answer
- Therefore, the complement of set A is:
\[ A' = \{1, 7, 8, 9, 10\} \]

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