Which of the following statements is/are True?

Question

(a) If $R$ is regular and $N$ is non-regular, then there exists $R+N$, which is regular.

(b) If $R$ is regular and $N$ is non-regular, then there exists $R+N$, which is non-regular.

Comments

what is + on a set? does it stand for union?

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yes..it is union

Answer 1

dont know what is + sign here because R and N used as SET.

if it is Union then ,

1. R= (a+b)*, N = a^nb^n , n>=0

R U N = (a+b)* which is regular.

2.R = phi, N = a^nb^n, n>=0

R U N = a^nb^n, n>=0

 

both are true (bcoz in options they said THERE EXIST )

(in general both are true but for a particular case where L and N is precisely given it may not holds true).

Comments

r1+r2=l1 unioin l2