True or False. Explain Briefly. (9). If L1 and L2 are not in D, then L1...

True or False. Explain Briefly.

(9). If L₁ and L₂ are not in D, then L₁ - L₂ cannot be regular.

(10). If L₁ and L₂ are not in D, then L₁ union L₂ cannot be in D.

(11). Every infinite language has a subset that is not in D.

(12). If not H were in D then every SD language would be in D.

Expert Solution

QUESTION NO 9:

False: It doesn't matter whether they are included in D or not this doesn't decide whether they are regular or not so the statement is incorrect. L1 - L2 are regular.

QUESTION NO 10:

False: If they don't belong to the D then it doesn't matter that L1 union L2 cannot be in D. There exists a possibility which negates the statement so the statement is false.

QUESTION NO 11:

True: The statement is true every infinite language has a subset that is not in D. D is not a super set which can have all the possible values. There are infinite times values so it is not possible that D contains all of them so the statement is true.

QUESTION NO 12:

True: The statement is true if not H were in D then every SD language would be in D. Then D will have all the possible pairs and it will be a complete SD language.

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