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Answer :
The statement is false because the regularity of a concatenation of two languages does not necessarily imply the regularity of both component languages separately. A non-regular language concatenated with a regular language containing only the empty string is a counterproof .Thus option 2.False is the correct answer.
The statement "if L1 L2 is regular, then L1 and L2 are necessarily regular" is false. To understand why, consider that the concatenation of two languages results in a new language. If L1 L2 is regular, it does not imply that both L1 and L2 must be regular languages individually. For example, if you have a non-regular language L1 and a regular language L2 that only contains the empty string, the concatenation of L1 and L2, which is just L1, could still be non-regular, even though L1 L2 is technically regular. This serves as counterproof to the statement.
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