Question

1.2 Which of the following statements is wrong?

       a). A set is a subset of itself

       b). Emptyset is a subset of any set

       c). A set is a subset of its powerset

       d). The cardinality of emptyset is 0

1.3. Which of the following statements is correct?

       a). A string is a set of symbols from an alphabet

       b). The length of the concatenation of two strings can

          be the same as one of them

       c). The length of a string is at least 1

       d). The concatenation of prefix and suffix of a string

  is itself

1.4 Which of the followings describe the regular expression    

       a). Any strings over alphabet  

       b). Any strings of even length over alphabet  

       c). , i.e., any strings consisting of two

          identical symbols

       c). , i.e., any strings consisting of an

          even number of identical symbols

1.5. Consider the following DFA

Which of the followings describes its language over ?

   a). All string that contain at most two a's

   b). All string that contain at least two a's

   c). All string that contain exactly two a's

   d). All strings that does not contain two a's  

1.6 Which of the following statements is correct?

       a). If and are both regular languages,  

          , then is also a regular language   

       b). If and are both regular languages, then

           is also a regular language

       c). If and are both regular languages,

          , then is also a regular language

        d). If and are both regular languages,

          , then is also a regular language   

1.7 Let be a regular language over alphabet . Which of the followings is correct?  

        a). It is possible that any subset of is not regular

        b). All strings of that has an even length is regular

        c). It is possible that for any , , is

        not regular

        d). The set of all strings that is formed by the

        concatenation of strings in may be nonregular

  1.8 Which of the followings is wrong?    

        a). A nondeterministic finite automaton is also a

        deterministic finite automaton.

        b). A deterministic finite automaton is also a

        nondeterministic finite automaton

        c). If a language is regular, then there exists a

        deterministic finite automaton such that the set of

        strings it accepts is exactly .  

        d). If a language is regular, then there exists a

        deterministic finite automaton such that the set of

        strings it does not accept is exactly .  

1.9 Consider the following NFA

Which of the following strings is not accepted by it?

      a).  

      b).   

      c).  

      d).  

1.10 Which of the following statement is wrong?

      a). The intersection of two non-regular languages can

      be regular.

      b). The union of two non-regular languages can be

      regular.

      c). The concatenation of two non-regular languages

      can be regular.

      d). The complement of a non-regular language can be

      regular.

Answer 1

1.2) b.

A set is a subset of itself and it's power set. The cardinality of empty set is zero.

1.3)d.

The length of concatenation of two strings is not the same as one of them and it is not necessary for the length of a string to be at least 1.A string is a finite set of symbols taken from alphabet.

1.4)a

Any strings which consists of an even number of identical symbols or has two identical symbols or is of even length over alphabet is not neccessarily a regular expression.

1.5)Insufficient Data

PLEASE LIKE THE ANSWER IF YOU FIND IT HELPFUL OR YOU CAN COMMENT IF YOU NEED CLARITY / EXPLANATION ON ANY POINT.