If U = {1,2,3,4,5,6},A = {1,2} , B = {3,4,5} , then :
(i) `A^(c)capB^(c)` =………..
(ii) `AuuB`=…………. .

Answer

To solve the given problem, we will follow the steps outlined below:

### Given:
- Universal set \( U = \{1, 2, 3, 4, 5, 6\} \)
- Set \( A = \{1, 2\} \)
- Set \( B = \{3, 4, 5\} \)

### (i) Finding \( A^{c} \cap B^{c} \)

**Step 1: Find \( A^{c} \) (the complement of A)**
The complement of set \( A \) consists of all elements in the universal set \( U \) that are not in \( A \).
\[ A^{c} = U - A = \{1, 2, 3, 4, 5, 6\} - \{1, 2\} = \{3, 4, 5, 6\} \]

**Step 2: Find \( B^{c} \) (the complement of B)**
Similarly, the complement of set \( B \) consists of all elements in the universal set \( U \) that are not in \( B \).
\[ B^{c} = U - B = \{1, 2, 3, 4, 5, 6\} - \{3, 4, 5\} = \{1, 2, 6\} \]

**Step 3: Find the intersection \( A^{c} \cap B^{c} \)**
The intersection of two sets contains all elements that are common to both sets.
\[ A^{c} \cap B^{c} = \{3, 4, 5, 6\} \cap \{1, 2, 6\} = \{6\} \]

### Answer for (i):
\[ A^{c} \cap B^{c} = \{6\} \]

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### (ii) Finding \( A \cup B \)

**Step 1: Find the union \( A \cup B \)**
The union of two sets contains all elements that are in either set.
\[ A \cup B = \{1, 2\} \cup \{3, 4, 5\} \]

**Step 2: Combine the elements of both sets**
Combining the elements, we get:
\[ A \cup B = \{1, 2, 3, 4, 5\} \]

### Answer for (ii):
\[ A \cup B = \{1, 2, 3, 4, 5\} \]

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### Summary of Answers:
(i) \( A^{c} \cap B^{c} = \{6\} \)
(ii) \( A \cup B = \{1, 2, 3, 4, 5\} \)

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