If P = {p : p is a letter in the word 'PERMANENT'}, find n(P).

Answer

To solve the problem, we need to find the number of unique letters in the word "PERMANENT". Let's go through the steps:

### Step 1: Identify the letters in the word "PERMANENT".
The letters in the word "PERMANENT" are: P, E, R, M, A, N, E, N, T.

### Step 2: List the letters without repetition.
Now, we will list the unique letters from the above list:
- P
- E
- R
- M
- A
- N
- T

Note that the letters 'E' and 'N' appear more than once, but we only count them once for the set.

### Step 3: Write the set in roster form.
The set P in roster form will be:
P = {P, E, R, M, A, N, T}

### Step 4: Count the number of elements in the set.
Now, we count the unique elements in the set P:
- P
- E
- R
- M
- A
- N
- T

There are a total of 7 unique letters.

### Step 5: State the final answer.
Thus, n(P), which represents the number of elements in the set P, is 7.

**Final Answer: n(P) = 7**

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