Given language: L = {ab U aba}*

To find:
- Minimum number of states (X) for a DFA
- Number of states (Y) to construct the NFA
- |X-Y|

Solution:
1. Constructing NFA for the language L:

- Start state q0
- Transition from q0 to q1 on input 'a'
- Transition from q1 to q2 on input 'b'
- Transition from q0 to q3 on input 'a'
- Transition from q3 to q4 on input 'b'
- Transition from q4 to q5 on input 'a'
- Final states: q2, q5

The diagram of the NFA for the language L is as follows:
```
a b a
q0 → q1 → q2, q3 → q4 → q5
↓ ↑
└───────┘
```
- The number of states in the NFA is 6. Therefore, Y = 6.

2. Conversion of NFA to DFA:

- The states of the DFA are the subsets of the states of the NFA.
- The start state of the DFA is the epsilon closure of the start state of the NFA.
- The transition function of the DFA is obtained by taking the epsilon closure of the states reached by each input symbol from the current state.
- The final states of the DFA are those subsets of the states of the NFA that contain a final state.

The conversion table is as follows:
```
DFA State | Input symbol | Next State
------------------+-----------------+--------------------------
A | a | B
A | b | C
B | a | B
B | b | D, C
C | a | B
C | b | C
D | a | B
D | b | C
------------------+-----------------+--------------------------
```
- The minimum number of states required for the DFA is 4. Therefore, X = 4.

3. |X-Y| = |4-6| = 2
- Therefore, the correct answer is option A (2).

Conclusion:
- The minimum number of states for a DFA is 4 and the number of states to construct the NFA is 6.
- The absolute difference between the two is 2.