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Important Examples: Identification of language

Identification of language:

Solutions:

You should know:

Before seeing the solution please follow the previous chapter to clear the concept How to identify language, Example 4,  Example 2.

Answer:

We know from the previous examples: Example 3 and Example 1. 

But in that case, the given problem is – 

Now, 

You should know:

Before seeing the solution please follow the previous chapter to clear the concept How to identify language, Example 1.

Answer:

This type of language we already discussed in the previous example Example 1 

But the only difference is the previous language asked for an even number and our given language asking for an odd number, still, both languages are the same type.

So, this given language is infinite language but there is no infinite comparison because m + n = odd is not a comparison even we can write regular expression for this language.

You should know:

Before seeing the solution please follow the previous chapter to clear the concept  How to identify language, Examples, Examples, Example 2.

Answer:

This same type of language we already discussed in previous examples like Example 2.

Now, if we follow our given example there is a condition but it is a finite condition 

i.e. p . q = 64 where 64 is a constant value. 

We know from previous examples that any language with finite conditions is always Regular Language.

You should know:

Before seeing the solution please follow the previous chapter to clear the concept How to identify language, Closer property of Regular Language.

Answer:

This language has one infinite comparison but we can identify this language in a different way.

As we know Regular Language is closed under complement for details see  Closer property of Regular Language.

Now, if the complement of any language is regular then, we can say this language is itself a regular language because regular language closed under complement.

So, it is another procedure that we should check before identifies any language. 

Now, we will check the complement of the given language is regular langue or not.

What is the complement of

Note:  In complement of the language, the range of the original language will be never changed example. 

Now,

You should know:

Before seeing the solution please follow the previous chapter to clear the concept How to identify language, Examples, Examples, Example 2.

Answer:

This same type of language we already discussed in the above examples like Example 3.

Now, if we follow our given example there is a condition but it is a finite condition 

i.e. p + q = 5 or we rewrite it as p = 5 – q where 5  is a constant value. 

We know from previous examples that any language with finite conditions is always Regular Language.