High School

In 4–6, describe L1L2, L1 ∪ L2, and (L1 ∪ L2)* for the given languages L1 and L2.


6. L1 is the set of all strings of 0’s and 1’s that start with a 0, and L2 is the set of all strings of 0’s and 1’s that end with a 0.

Answer :

L1L2 consists of all strings that start with a 0 and end with a 0. L1 ∪ L2 consists of all strings that either start with a 0, end with a 0, or both. (L1 ∪ L2)* consists of all possible concatenations of zero or more strings that start with a 0 or end with a 0, or both, including the empty string.

1. L1L2 (Concatenation):

L1L2 represents the concatenation of the languages L1 and L2. In this case, L1L2 would consist of all strings that can be formed by concatenating a string from L1 with a string from L2.

For the given languages L1 and L2, L1L2 would consist of all strings that start with a 0 and end with a 0. Since L1 contains strings that start with 0 and L2 contains strings that end with 0, the concatenation of L1 and L2 will yield strings that satisfy both properties.

2. L1 ∪ L2 (Union):

L1 ∪ L2 represents the union of the languages L1 and L2. It consists of all strings that belong to either L1 or L2, or both.

For the given languages L1 and L2, L1 ∪ L2 would consist of all strings that start with a 0 or end with a 0, or satisfy both conditions. In other words, it includes all strings that either start with a 0, end with a 0, or both.

3. (L1 ∪ L2)* (Kleene Star):

(L1 ∪ L2)* represents the Kleene star operation on the union of L1 and L2. It consists of all possible concatenations of zero or more strings from L1 and L2.

For the given languages L1 and L2, (L1 ∪ L2)* would consist of all strings that can be formed by concatenating zero or more strings that start with a 0 or end with a 0, or both. It includes the empty string, as well as any combination of strings from L1 and L2 that satisfy the given conditions.

Learn more about union here:

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