Let `A={a, b, d, e}=B={c, d, f, m}, C={a, l, m, o}`. Then `C nn(Auu B)` will be given by

Options

A. `{a, l, m, o}`
B. `{b, c, l, o}`
C. `{a, m}`
D. `{a, b, c, d, f, l, m, o}`

Answer

To solve the problem, we need to find \( C \cap (A \cup B) \). Let's break it down step by step.

### Step 1: Identify the sets
We have the following sets:
- \( A = \{a, b, d, e\} \)
- \( B = \{c, d, f, m\} \)
- \( C = \{a, l, m, o\} \)

### Step 2: Find \( A \cup B \)
The union of two sets \( A \) and \( B \) includes all elements from both sets without duplication.

- Elements in \( A \): \( a, b, d, e \)
- Elements in \( B \): \( c, d, f, m \)

Now, combine these sets:
- \( A \cup B = \{a, b, d, e\} \cup \{c, d, f, m\} \)

Since \( d \) is common in both sets, we only include it once:
- \( A \cup B = \{a, b, c, d, e, f, m\} \)

### Step 3: Find \( C \cap (A \cup B) \)
Now, we need to find the intersection of set \( C \) with the union \( A \cup B \).

- Elements in \( C \): \( a, l, m, o \)
- Elements in \( A \cup B \): \( a, b, c, d, e, f, m \)

Now, we find the common elements:
- The common elements between \( C \) and \( A \cup B \) are \( a \) and \( m \).

Thus,
- \( C \cap (A \cup B) = \{a, m\} \)

### Final Answer
The final answer is \( \{a, m\} \).

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