Final answer:
The number of relations on the set x={1,2,3,4,5} is 3125.
Step-by-step explanation:
A relation on a set can be thought of as a set of ordered pairs, where the first element of each pair is an element from the set and the second element can be any element from the set. In this case, the set is x = {1, 2, 3, 4, 5}. To find the number of relations on x with given conditions, we need to consider the number of choices for each element in the set and multiply them together. Since each element can be related to any other element or itself, we have 5 choices for each element. Therefore, the total number of relations on x is 5^5 = 3125.