Which of the following statements are true and which false ?
`{:((i),0 in{},(ii),0in{0},(iii),0in{(0)}),((iv),0in{0,{0}},(v),{0}in{0},,):}`

Answer

To determine which of the statements are true and which are false, we will analyze each statement one by one.

### Given Statements:
1. \( 0 \in \{\} \)
2. \( 0 \in \{0\} \)
3. \( 0 \in (0) \)
4. \( 0 \in \{0, 0\} \)
5. \( \{0\} \in \{0\} \)

### Step-by-Step Analysis:

1. **Statement (i): \( 0 \in \{\} \)**
- The set \(\{\}\) is an empty set, which contains no elements.
- Therefore, \(0\) cannot be an element of an empty set.
- **Conclusion:** This statement is **False**.

2. **Statement (ii): \( 0 \in \{0\} \)**
- The set \(\{0\}\) contains exactly one element, which is \(0\).
- Therefore, \(0\) is indeed an element of the set \(\{0\}\).
- **Conclusion:** This statement is **True**.

3. **Statement (iii): \( 0 \in (0) \)**
- The notation \((0)\) typically represents a single value (not a set) and not a set containing \(0\).
- Therefore, \(0\) cannot be an element of something that is not a set.
- **Conclusion:** This statement is **False**.

4. **Statement (iv): \( 0 \in \{0, 0\} \)**
- The set \(\{0, 0\}\) is equivalent to \(\{0\}\) because sets do not consider duplicate elements.
- Therefore, \(0\) is an element of the set \(\{0, 0\}\).
- **Conclusion:** This statement is **True**.

5. **Statement (v): \( \{0\} \in \{0\} \)**
- The set \(\{0\}\) contains the element \(0\), but it does not contain the set \(\{0\}\) itself as an element.
- Therefore, \(\{0\}\) is not an element of \(\{0\}\).
- **Conclusion:** This statement is **False**.

### Summary of Results:
- (i) False
- (ii) True
- (iii) False
- (iv) True
- (v) False

### Final Answer:
- True Statements: (ii), (iv)
- False Statements: (i), (iii), (v)