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NFA Example: Consider The NFA M Given Below

Consider The NFA M Given Below

Let ‘M’ Be The NFA Obtain From M By Converting All The Non-Final States Into Final States

If L & LBe The Language Accepted  By M And MThen Which Of The Following Statement Is Correct.

a) L=L1

b) L⊂L1

c) L1⊂L

d) L∩L1

e) L∪L1=Σ*

f) None

 

Before Solving This Problem I’ll Tell Yo What I Explained Before So That You’ll Understand This Problem Easily.

In Previous Problems I Solved I Tried To Take Complement For NFA.

But

Complement For NFA Is Not Possible.

Because

The Language We Get After Giving Complement To DFA, That Is The Complement For The Language DFA.

 

For Example, There Are Two Languages L& L2

L1              L2

If L11  Is LSo, The Strings In LWill Not Be There In LAnd The Strings In L2Will Not Be There In L1

This Is Called Proper Complement

This Case Will Not Be There In NFA

 

Solution:-

Question Asked Is M1

Be The The NFA Obtain From M By Converting All The Non-Final States Into Final State

Here Question Is To COnvert Non-Final To Final.

Means All Non-Final States Becomes Final.

It Is Not Interchanging Non-Final To Final And Final To Non-Final

a) L=L1

L={ε,0………} // String Must Start With ‘0’

L1={ε,0………} // String Is Starting With ‘0’

Two Languages Are Same L=LSatisfied

 

b) L⊂L1

L={ε,0………}

L1={ε,0………}

If Two Languages Are Same The L Will Be The Subset Of LContains ‘L’

 

c) L1⊂L

L={ε,0………}

L1={ε,0………}

Two Languages Are Same, So Obviously LWill Be The Subset Of L

 

d) L∩L1

L={ε,0………}

L1={ε,0………}

Two Languages Are Same, So L And LIs Not Equal To Φ

 

e) L∪L1=Σ*

L={ε,0………}

L1={ε,0………}

Σ*=Universal Language

Two Languages Are Same

Two Languages Are Starting With ‘0’ Only But In Universal Language

It Can Start With ‘1’ Also

So This Statement Is False

 

f) None

Wrong

 

 

 

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