Question 64: An annihilator for an operator is a value such that when the operator is applied to the annihilator and some other value, the result is the annihilator. For example in arithmetic 0 is the annihilator for multiplication (0*x = 0). An identity for an operator is a value such that when the operator is applied to the identity and some other value, the result is the other value. Similarly, 0 is the identity for addition and 1 for multiplication (0+x = x and 1*x = x).
Which of the following is true for regular expressions?
- ∅ + L = L
- ∅L = ∅
- ∈L = L
- All of the above
Solution: ∈ is the identity for concatenation operation, and ∅ is the annihilator for concatenation and identity for union. The correct answer is option 4