State whether the following pairs of sets are equal or not :
A={x|x is a letter in the word SOPHIA}
B = {x|x is a letter in the word MUMTAZ}

Answer

To determine whether the sets A and B are equal, we need to identify the elements in each set and then compare them.

### Step 1: Identify the elements of Set A
Set A is defined as:
\[ A = \{ x \mid x \text{ is a letter in the word SOPHIA} \} \]

Let's list the letters in the word "SOPHIA":
- The letters are: S, O, P, H, I, A.

Now, we write down the unique letters in Set A:
\[ A = \{ S, O, P, H, I, A \} \]

### Step 2: Identify the elements of Set B
Set B is defined as:
\[ B = \{ x \mid x \text{ is a letter in the word MUMTAZ} \} \]

Let's list the letters in the word "MUMTAZ":
- The letters are: M, U, M, T, A, Z.

Now, we write down the unique letters in Set B:
\[ B = \{ M, U, T, A, Z \} \]

### Step 3: Compare the elements of Set A and Set B
Now we compare the elements of both sets:
- Set A: \( \{ S, O, P, H, I, A \} \)
- Set B: \( \{ M, U, T, A, Z \} \)

### Step 4: Determine if the sets are equal
For two sets to be equal, they must contain exactly the same elements.

- Set A contains the letters S, O, P, H, I, A.
- Set B contains the letters M, U, T, A, Z.

Since the elements in Set A and Set B are not the same (for example, S and O are in Set A but not in Set B, and M, U, T, Z are in Set B but not in Set A), we conclude that:

\[ A \neq B \]

### Final Conclusion
The sets A and B are not equal.

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