Let M={letters of the word REAL} and N={letters of the word LARE}. Write sets M and N in roster form and then state whether:
(i) `M sube N` is true.
(ii) `N sube M` is true.
(iii) M=C is true.

Answer

To solve the problem, we need to follow these steps:

### Step 1: Identify the sets M and N in roster form.

**Set M**: The letters of the word "REAL" are R, E, A, L.
So, in roster form, we write:
\[ M = \{ R, E, A, L \} \]

**Set N**: The letters of the word "LARE" are L, A, R, E.
So, in roster form, we write:
\[ N = \{ L, A, R, E \} \]

### Step 2: Check if \( M \subseteq N \) is true.

To determine if \( M \subseteq N \) (M is a subset of N), we need to check if every element in M is also in N.

- Elements of M: R, E, A, L
- Elements of N: L, A, R, E

Since all elements of M (R, E, A, L) are present in N, we conclude that:
\[ M \subseteq N \text{ is true.} \]

### Step 3: Check if \( N \subseteq M \) is true.

Now, we check if \( N \subseteq M \) (N is a subset of M).

- Elements of N: L, A, R, E
- Elements of M: R, E, A, L

Since all elements of N (L, A, R, E) are present in M, we conclude that:
\[ N \subseteq M \text{ is true.} \]

### Step 4: Check if \( M = N \) is true.

To determine if \( M = N \), we check if both sets contain exactly the same elements.

- Set M: {R, E, A, L}
- Set N: {L, A, R, E}

Since both sets contain the same elements, we conclude that:
\[ M = N \text{ is true.} \]

### Summary of Results:
1. \( M \subseteq N \) is true.
2. \( N \subseteq M \) is true.
3. \( M = N \) is true.