f L1 and L2′ are regular languages, L1 ∩∩ (L2′ U L1′)’ will be _____.a)all of the mentionedb)may be regularc)regulard)none of the mentionede)non regular

The answer is (c) regular.

Here's the step-by-step explanation:

1. Regular languages are closed under the operations of union, intersection, and complement. This means that if you take two regular languages and perform any of these operations, the result will still be a regular language.

2. L1 and L2' are given as regular languages.

3. L1' is the complement of L1, which is also a regular language because regular languages are closed under complement.

4. L2' U L1' is the union of L2' and L1', which is also a regular language because regular languages are closed under union.

5. (L2' U L1')' is the complement of the union, which is also a regular language because regular languages are closed under complement.

6. Finally, L1 ∩ (L2' U L1')' is the intersection of L1 and the complement of the union, which is also a regular language because regular languages are closed under intersection.

So, the result of these operations will always be a regular language.