If A = {letters of word ORANGE } and B = { letters of word MANGO} , find
`A cup B `

Answer

To solve the problem of finding the union of the sets A and B, we will follow these steps:

### Step 1: Identify the elements of set A
Set A consists of the letters of the word "ORANGE".
- The letters are: O, R, A, N, G, E.
- Therefore, we can write:
\[ A = \{ O, R, A, N, G, E \} \]

### Step 2: Identify the elements of set B
Set B consists of the letters of the word "MANGO".
- The letters are: M, A, N, G, O.
- Therefore, we can write:
\[ B = \{ M, A, N, G, O \} \]

### Step 3: Find the union of sets A and B
The union of two sets, denoted as \( A \cup B \), includes all the unique elements from both sets. We will combine the elements from both sets and remove any duplicates.

- From set A, we have: O, R, A, N, G, E
- From set B, we have: M, A, N, G, O

Now, we will combine these elements:
- Combine: O, R, A, N, G, E, M, A, N, G, O

### Step 4: Remove duplicates
Now we will list the unique elements:
- Unique elements are: O, R, A, N, G, E, M

Thus, we can write the union of sets A and B as:
\[ A \cup B = \{ O, R, A, N, G, E, M \} \]

### Final Answer
The union of sets A and B is:
\[ A \cup B = \{ O, R, A, N, G, E, M \} \]

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