Which of the following statements are true or false ?
(i) `{a,e,o}={i,u,o}`
(ii) `{5,1,3}={1,3,5}`
(iii) `{x:x inR ,x` is multiple of 5 } = {5,10,15,20,……..}
(iv) {x:x is an even prime } = {2}.

Answer

To determine whether the given statements about sets are true or false, we will analyze each statement one by one.

### Solution:

1. **Statement (i):** `{a, e, o} = {i, u, o}`
- To check if two sets are equal, we need to see if they contain the same elements.
- The first set `{a, e, o}` contains the elements `a`, `e`, and `o`.
- The second set `{i, u, o}` contains the elements `i`, `u`, and `o`.
- Comparing the elements, we see that the first set has `a` and `e`, which are not present in the second set. Therefore, the two sets are not equal.
- **Conclusion:** This statement is **False**.

2. **Statement (ii):** `{5, 1, 3} = {1, 3, 5}`
- Again, we check for equality by comparing the elements of both sets.
- The first set `{5, 1, 3}` contains `5`, `1`, and `3`.
- The second set `{1, 3, 5}` contains `1`, `3`, and `5`.
- Both sets contain the same elements, just in a different order. In set theory, the order of elements does not matter.
- **Conclusion:** This statement is **True**.

3. **Statement (iii):** `{x : x ∈ R, x is a multiple of 5} = {5, 10, 15, 20, ...}`
- The left side describes the set of all real numbers that are multiples of 5.
- The right side lists specific multiples of 5: `5`, `10`, `15`, `20`, and so on.
- The left side includes all multiples of 5, which can be represented as `{5n : n ∈ Z}` where `Z` is the set of integers. This includes numbers like `-5`, `0`, `5`, `10`, `15`, etc.
- Since the right side does not include negative multiples or zero, the two sets are not equal.
- **Conclusion:** This statement is **False**.

4. **Statement (iv):** `{x : x is an even prime} = {2}`
- The left side describes the set of even prime numbers.
- The only even prime number is `2`, as all other even numbers are not prime (they are divisible by 2).
- Thus, the left side contains only the element `2`, which matches the right side.
- **Conclusion:** This statement is **True**.

### Final Results:
- (i) False
- (ii) True
- (iii) False
- (iv) True