Suggest a universal set for the sets given below :

[ odd number less than 8], [Prime numbers less than 8] and (even numbers between 3 and 8 ].

Answer

To suggest a universal set for the given sets, we will follow these steps:

### Step 1: Identify the sets
1. **Set A**: Odd numbers less than 8
2. **Set B**: Prime numbers less than 8
3. **Set C**: Even numbers between 3 and 8

### Step 2: Determine the elements of each set
- **Set A**: The odd numbers less than 8 are 1, 3, 5, and 7.
- So, \( A = \{1, 3, 5, 7\} \)

- **Set B**: The prime numbers less than 8 are 2, 3, 5, and 7.
- So, \( B = \{2, 3, 5, 7\} \)

- **Set C**: The even numbers between 3 and 8 are 4 and 6.
- So, \( C = \{4, 6\} \)

### Step 3: Combine all elements to form the universal set
To form the universal set \( U \), we will take all unique elements from sets A, B, and C.

- From Set A: 1, 3, 5, 7
- From Set B: 2, 3, 5, 7 (3, 5, and 7 are already included)
- From Set C: 4, 6 (these are new)

Now, combining all unique elements:
- \( U = \{1, 2, 3, 4, 5, 6, 7\} \)

### Final Answer
The universal set \( U \) is:
\[ U = \{1, 2, 3, 4, 5, 6, 7\} \]

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