If `A = {1, 4, 7, 8}, B= {4, 6, 8, 9} and C= {3, 4, 5, 7}` be three subsets of a universal set U= {1,2,3,4,5,6,7,8,9}. Then `A uu (B nn C')` is equal to

Options

A. `{1,6,7,8,9}`
B. `{1,6,7,8,9,3}`
C. `{1,4,6,7,8,9}`
D. None of these

Answer

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

- \( A = \{1, 4, 7, 8\} \)
- \( B = \{4, 6, 8, 9\} \)
- \( C = \{3, 4, 5, 7\} \)
- The universal set \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \)

### Step 1: Find \( C' \) (the complement of set C)

The complement of set \( C \) is found by subtracting the elements of \( C \) from the universal set \( U \).

\[ C' = U - C = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} - \{3, 4, 5, 7\} \]

The elements left in \( C' \) are:

\[ C' = \{1, 2, 6, 8, 9\} \]

### Step 2: Find \( B \cap C' \) (the intersection of sets B and C')

Now we find the intersection of sets \( B \) and \( C' \):

\[ B = \{4, 6, 8, 9\} \]
\[ C' = \{1, 2, 6, 8, 9\} \]

The common elements in \( B \) and \( C' \) are:

\[ B \cap C' = \{6, 8, 9\} \]

### Step 3: Find \( A \cup (B \cap C') \) (the union of sets A and \( B \cap C' \))

Now we find the union of set \( A \) and the result from step 2:

\[ A = \{1, 4, 7, 8\} \]
\[ B \cap C' = \{6, 8, 9\} \]

The union combines all unique elements from both sets:

\[ A \cup (B \cap C') = \{1, 4, 7, 8\} \cup \{6, 8, 9\} \]

The unique elements are:

\[ A \cup (B \cap C') = \{1, 4, 6, 7, 8, 9\} \]

### Final Result

Thus, the final result is:

\[ A \cup (B \cap C') = \{1, 4, 6, 7, 8, 9\} \]