regular Languages

Question 1

Which of the following definitions below generates the same language as L, where L = {xnyn such that n >= 1}? 

 I. E → xEy|xy
 II. xy|(x+xyy+)
 III. x+y+
A
I only
B
I and II
C
II and III
D
II only
Theory-of-ComputationRegular LanguagesGATE 1995
Question 1 Explanation: 
(I) is the correct definition and the other two is wrong because the other two can have any no. of x and y. There is no such restriction over the number of both being equal.
Question 2

Let Σ = {0,1}, L = Σ* and R = {0n1n such that n >0} then the languages L ∪ R and R are respectively

A
regular, regular
B
not regular, regular
C
regular, not regular
D
not regular, no regular
Theory-of-Computationregular LanguagesGATE 1995
Question 2 Explanation: 
L∪R is nothing but L itself. Because R is subset of L and hence regular. R is deterministic context free but not regular as we require a stack to keep the count of 0's to make that of 1's.
There are 2 questions to complete.

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