Let `A= {1,2,3,4}, B= {2,3,5,7} and C{1,3,5,6}`. Then, the value of `A nn (B uu C)` is

Options

A. `{1,2,3}`
B. `{1,2}`
C. `{3,5,6}`
D. `{2,3,4}`

Answer

To solve the problem, we need to find the value of \( A \cap (B \cup C) \) where:

- \( A = \{1, 2, 3, 4\} \)
- \( B = \{2, 3, 5, 7\} \)
- \( C = \{1, 3, 5, 6\} \)

### Step 1: Calculate \( B \cup C \)

The union of two sets \( B \) and \( C \) includes all elements that are in either set.

- Elements in \( B \): \( 2, 3, 5, 7 \)
- Elements in \( C \): \( 1, 3, 5, 6 \)

Now, we combine these elements, ensuring we list each unique element only once:

\[ B \cup C = \{1, 2, 3, 5, 6, 7\} \]

### Step 2: Calculate \( A \cap (B \cup C) \)

Now we need to find the intersection of set \( A \) with the union we just calculated \( B \cup C \).

- Elements in \( A \): \( 1, 2, 3, 4 \)
- Elements in \( B \cup C \): \( 1, 2, 3, 5, 6, 7 \)

The intersection includes only those elements that are present in both sets:

- Common elements between \( A \) and \( B \cup C \): \( 1, 2, 3 \)

Thus, we have:

\[ A \cap (B \cup C) = \{1, 2, 3\} \]

### Final Answer

The value of \( A \cap (B \cup C) \) is \( \{1, 2, 3\} \).

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