Context Free language

Question

If L₁ is context free and L₂ is not context free, then L₁ ∩ L₂ is context free.

Is this true or not?

Answer 1

No..in worst case it will not be CFL..

L1 intersection L2= higher order language among two..

Comments

that's right way..

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suppose if L2 was CSL?? then what would be intersection of the two?? CSL??

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As per my understanding for union highest of two languages is the resultant language

For intersection lowest of two languages (but not always true)

I'm I wrong

Answer 2

take an example

L1= (a^n b^n | where n >=1  )   //CFL

L2=(a^n b^n c^n| where n >=1 )  // NCFL

there intersection are not CFL

BUT if

L1= (a^n b^n | where n >=0  )   //CFL

L2=(a^n b^n c^n| where n >=0 )  // NCFL

then there intersection will be empty language which is regular which is CFL

hence we may contradict here

 

BUT we always need do focus on worst case

so this statement is FALSE