Regular Languages and finite automata

Question 1

Let L be a regular language and M be a context-free language, both over the alphabet Σ. Let Lc and Mc denote the complements of L and M respectively. Which of the following statements about the language if Lc ∪ Mc is TRUE?

A
It is necessarily regular but not necessarily context-free.
B
It is necessarily context-free.
C
It is necessarily non-regular.
D
None of the above.
Theory-of-ComputationRegular Languages and finite automataGATE 2005-IT
Question 1 Explanation: 
Context-free languages not closed under complementation. So, Lc ∪ Mc is neither regular nor context-free. It might be context sensitive language.
Question 2

Which of the following statements is TRUE about the regular expression 01*0?

A
It represents a finite set of finite strings.
B
It represents an infinite set of finite strings.
C
It represents a finite set of infinite strings.
D
It represents an infinite set of infinite strings.
Theory-of-ComputationRegular languages and finite automataGATE 2005-IT
Question 2 Explanation: 
The given expression 01*0 is regular. So this is a finite string. So options C and D are false and * is placed. So this is infinite set.
So, given regular expression represents an infinite set of finite strings.
There are 2 questions to complete.

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