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.

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