If `A= {a, b, c, d} andB = {b, c, e}`, then `A cup B` is equal to

Options

A. `{ a, b, c, d , e}`
B. `phi`
C. `{ b, c, d }`
D. None of these

Answer

To solve the problem of finding \( A \cup B \) where \( A = \{a, b, c, d\} \) and \( B = \{b, c, e\} \), we will follow these steps:

### Step 1: Identify the elements in set A and set B
- Set \( A \) contains the elements: \( a, b, c, d \)
- Set \( B \) contains the elements: \( b, c, e \)

### Step 2: Write down the union of sets A and B
The union of two sets, denoted as \( A \cup B \), includes all unique elements from both sets.

### Step 3: Combine the elements from both sets
- From set \( A \): \( a, b, c, d \)
- From set \( B \): \( b, c, e \)

### Step 4: List all unique elements
Now, we will combine the elements and ensure that we only include unique elements:
- Start with elements from set \( A \): \( a, b, c, d \)
- Add elements from set \( B \): \( b \) and \( c \) are already included, so we only add \( e \).

### Step 5: Write the final union set
Thus, the union \( A \cup B \) will be:
\[ A \cup B = \{a, b, c, d, e\} \]

### Final Answer
The union of sets \( A \) and \( B \) is \( \{a, b, c, d, e\} \).

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