Fur each of the folowing parts eithee give a langonge A that

Fur each of the folowing parts, eithee give a langonge A that hoe the did p aed esplain why it han the properties, or eoxplain why no nuch langin ess that the, alphalet -(0,1). (a) A is not a regular langcunge, and A Sm B, whee B-1 0). (b) A is not decidable language, and A Sm B, where B = {0\"1\"lms (e) A is not a decidable language, and B Sn A where B = (r1mjm 20).

Solution

Since your image is not clear am answering as per what i have understood.

1)To prove a language is not regualr there are generaly two main types:

Using pumping lemma

Proving the properties of regular language is not satisfied.

Letme use the first method:

B= 0*1* be the language

First let B be a regular language.

Now p be the pumping length of the pumping lemma.

Now we should take a word which is also in the form of regular language B but greater than the length of pumping lemma (p).

: 000 111

Now spilt the word into three parts xyz with

|xy|n

|y|>0

Since |xy|<p, However we divide it x consist of 0 and y consist of 1 . Now assume x = h and y=k ; h>=0, k>=1

h+k >=p

take i=0 and consider zxyⁱ=xz. this word is NOT in B since it is of the form 0^n-k 1^k hence this is not a regular language