If U={1,2,3,4,5,6,7,8}
A={3,4,5,6} and B={1,3,5,7} then the value of (A'-B') is

Options

A. `{2,8}`
B. `{3,5}`
C. `{1,7}`
D. `{1,2,4,6}`

Answer

To solve the problem, we need to find the value of \( A' - B' \), where \( A' \) is the complement of set \( A \) and \( B' \) is the complement of set \( B \). Let's go through the steps systematically.

### Step 1: Identify the Universal Set and Given Sets
The universal set \( U \) is given as:
\[ U = \{1, 2, 3, 4, 5, 6, 7, 8\} \]
The set \( A \) is given as:
\[ A = \{3, 4, 5, 6\} \]
The set \( B \) is given as:
\[ B = \{1, 3, 5, 7\} \]

### Step 2: Find the Complement of Set A
The complement of set \( A \), denoted as \( A' \), consists of all elements in the universal set \( U \) that are not in \( A \).
\[ A' = U - A \]
Calculating \( A' \):
- Elements in \( U \) but not in \( A \) are \( 1, 2, 7, 8 \).
Thus,
\[ A' = \{1, 2, 7, 8\} \]

### Step 3: Find the Complement of Set B
The complement of set \( B \), denoted as \( B' \), consists of all elements in the universal set \( U \) that are not in \( B \).
\[ B' = U - B \]
Calculating \( B' \):
- Elements in \( U \) but not in \( B \) are \( 2, 4, 6, 8 \).
Thus,
\[ B' = \{2, 4, 6, 8\} \]

### Step 4: Find the Difference \( A' - B' \)
Now, we need to find the set difference \( A' - B' \), which includes elements that are in \( A' \) but not in \( B' \).
\[ A' - B' = \{1, 2, 7, 8\} - \{2, 4, 6, 8\} \]
- From \( A' \), we remove the elements that are in \( B' \):
- \( 1 \) is in \( A' \) and not in \( B' \) (include)
- \( 2 \) is in both \( A' \) and \( B' \) (remove)
- \( 7 \) is in \( A' \) and not in \( B' \) (include)
- \( 8 \) is in both \( A' \) and \( B' \) (remove)

Thus, the resulting set is:
\[ A' - B' = \{1, 7\} \]

### Final Answer
The value of \( A' - B' \) is:
\[ \{1, 7\} \]

---