A and B are two events such that `P(A)=0.54, P(B)=0.69` and `P(AnnB)=0.535`.
(i) `P(AuuB)` (ii) `P(A'nnB')`
(iii) `P(AnnB')` (iv) `P(BnnA')`

Explanation

To solve the problem, we need to find the probabilities of four different events based on the given probabilities of events A and B.

Given:
- \( P(A) = 0.54 \)
- \( P(B) = 0.69 \)
- \( P(A \cap B) = 0.535 \)

We will find:
(i) \( P(A \cup B) \)
(ii) \( P(A' \cap B') \)
(iii) \( P(A \cap B') \)
(iv) \( P(B \cap A') \)

### Step-by-Step Solution:

**(i) Finding \( P(A \cup B) \)**

Using the formula for the union of two events:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Substituting the values:
\[ P(A \cup B) = 0.54 + 0.69 - 0.535 \]
\[ P(A \cup B) = 1.23 - 0.535 = 0.695 \]

**(ii) Finding \( P(A' \cap B') \)**

Using De Morgan's law:
\[ P(A' \cap B') = 1 - P(A \cup B) \]

Substituting the value we found in part (i):
\[ P(A' \cap B') = 1 - 0.695 = 0.305 \]

**(iii) Finding \( P(A \cap B') \)**

Using the formula:
\[ P(A \cap B') = P(A) - P(A \cap B) \]

Substituting the values:
\[ P(A \cap B') = 0.54 - 0.535 = 0.005 \]

**(iv) Finding \( P(B \cap A') \)**

Using the formula:
\[ P(B \cap A') = P(B) - P(A \cap B) \]

Substituting the values:
\[ P(B \cap A') = 0.69 - 0.535 = 0.155 \]

### Final Answers:
1. \( P(A \cup B) = 0.695 \)
2. \( P(A' \cap B') = 0.305 \)
3. \( P(A \cap B') = 0.005 \)
4. \( P(B \cap A') = 0.155 \)