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

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the sets A and B
- Set A consists of the letters of the word "ORANGE".
- Set B consists of the letters of the word "MANGO".

### Step 2: List the elements of each set
- For Set A (ORANGE):
- The letters are {O, R, A, N, G, E}.

- For Set B (MANGO):
- The letters are {M, A, N, G, O}.

### Step 3: Count the number of elements in each set
- The number of elements in Set A, denoted as n(A):
- n(A) = 6 (since there are 6 unique letters: O, R, A, N, G, E).

- The number of elements in Set B, denoted as n(B):
- n(B) = 5 (since there are 5 unique letters: M, A, N, G, O).

### Step 4: Find the union of sets A and B
- The union of sets A and B, denoted as A ∪ B, includes all unique elements from both sets:
- A ∪ B = {O, R, A, N, G, E, M} (combine all unique letters).

- Count the number of elements in the union:
- n(A ∪ B) = 7 (the unique letters are O, R, A, N, G, E, M).

### Step 5: Find the intersection of sets A and B
- The intersection of sets A and B, denoted as A ∩ B, includes only the elements that are common to both sets:
- A ∩ B = {O, A, N, G} (these letters are present in both sets).

- Count the number of elements in the intersection:
- n(A ∩ B) = 4 (the common letters are O, A, N, G).

### Final Results
- n(A) = 6
- n(B) = 5
- n(A ∪ B) = 7
- n(A ∩ B) = 4

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