Which of the following is/are true ?

Options

A. If M=N , then M' = N'
B. If M' = N' , then M = N .
C. Both (a) and (b)
D. Neither (a) nor (b)

Answer

To determine which of the statements regarding sets \( m \) and \( n \) are true, let's analyze the statements step by step.

### Step 1: Understanding the Complement of Sets
The complement of a set \( m \) (denoted as \( m' \)) is defined as the universal set \( U \) minus the set \( m \). Therefore, we can express the complement of \( m \) and \( n \) as:
- \( m' = U - m \)
- \( n' = U - n \)

### Step 2: Analyzing Statement 1
The first statement claims that if sets \( m \) and \( n \) are equal (\( m = n \)), then their complements \( m' \) and \( n' \) will also be equal.

Since \( m = n \), we can substitute \( n \) with \( m \):
- \( n' = U - n = U - m \)

Thus, we have:
- \( m' = U - m \)
- \( n' = U - m \)

Since both \( m' \) and \( n' \) are equal to \( U - m \), we conclude that:
- \( m' = n' \)

**Conclusion for Statement 1**: True.

### Step 3: Analyzing Statement 2
The second statement claims that if the complements \( m' \) and \( n' \) are equal, then the sets \( m \) and \( n \) must also be equal.

Assuming \( m' = n' \), we can write:
- \( U - m = U - n \)

By rearranging this equation, we can cancel the universal set \( U \) from both sides:
- \( -m = -n \)

This implies:
- \( m = n \)

**Conclusion for Statement 2**: True.

### Final Conclusion
Both statements are true. Therefore, the correct answer is that both statement 1 and statement 2 are true.