test series

Question

If L₁ and L₂ are non-regular, then L₁ ⋃ L₂ is also non-regular.

state the above statement is true or false?

Comments

False..

L1=a^nb^m | n=m

L2=a^nb^m| n not equal to m

Both are CFL

But their union gives a*b* which is regular.

Answer 1

let L1= a^m b^n m,n>=1 m>=n   non regular

let l2=a^m b^n m,n>=1 m<n non regular

union l3= a^m b^n m,n>=1 m>=n or m<n}

equivalent to{ a^m b^n m,n>=1 } is regular