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 (Bnn 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 \( A = \{1, 4, 7, 8\} \), \( B = \{4, 6, 8, 9\} \), \( C = \{3, 4, 5, 7\} \), and the universal set \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \).

### Step-by-Step Solution:

1. **Find the Complement of Set C**:
The complement of set \( C \) (denoted as \( C' \)) consists of all the elements in the universal set \( U \) that are not in \( C \).
\[ C' = U - C = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} - \{3, 4, 5, 7\} \]
Removing the elements of \( C \) from \( U \):
\[ C' = \{1, 2, 6, 8, 9\} \]

2. **Find the Intersection of Set B and C'**:
Now we need to find the intersection \( B \cap C' \).
\[ B = \{4, 6, 8, 9\} \]
The intersection consists of elements that are common to both \( B \) and \( C' \):
\[ B \cap C' = \{4, 6, 8, 9\} \cap \{1, 2, 6, 8, 9\} \]
The common elements are:
\[ B \cap C' = \{6, 8, 9\} \]

3. **Find the Union of Set A and (B ∩ C')**:
Now we need to find \( A \cup (B \cap C') \):
\[ A = \{1, 4, 7, 8\} \]
We combine the elements of \( A \) and \( B \cap C' \):
\[ A \cup (B \cap C') = \{1, 4, 7, 8\} \cup \{6, 8, 9\} \]
In the union, we take all unique elements:
\[ A \cup (B \cap C') = \{1, 4, 6, 7, 8, 9\} \]

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