Let A = [2,4,6,8 ],B = { 6,8,10 ,12} and C = {7,8,9,10 } Find .
` B uu C `

Answer

To find \( B \cup C \) (the union of sets B and C), we will follow these steps:

### Step 1: Identify the elements in each set
- Set B contains the elements: \( \{6, 8, 10, 12\} \)
- Set C contains the elements: \( \{7, 8, 9, 10\} \)

### Step 2: Write down the elements of both sets
- From set B, we have: \( 6, 8, 10, 12 \)
- From set C, we have: \( 7, 8, 9, 10 \)

### Step 3: Combine the elements from both sets
- We will combine the elements from both sets, ensuring that we do not repeat any elements.
- Starting with set B: \( 6, 8, 10, 12 \)
- Now, add the elements from set C: \( 7, 8, 9, 10 \)

### Step 4: Remove duplicates
- The combined elements are: \( 6, 8, 10, 12, 7, 9 \)
- Notice that \( 8 \) and \( 10 \) are present in both sets, so we will only include them once.

### Step 5: Write the final union set
- Therefore, the union \( B \cup C \) is: \( \{6, 7, 8, 9, 10, 12\} \)

### Final Answer:
\[ B \cup C = \{6, 7, 8, 9, 10, 12\} \]

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