This is a question in my text book that I cannot understand the solution provided for that:
In each case below, give a simple descreption of the smallest set of languages that contains all the "basic" languages $\varnothing$,$\{\Lambda\}$, and $\{\sigma\}$ (for every $\sigma \in \Sigma$) and is closed under the specefied operation.
- Union
- Concatenation
- Union and Concatentation
Here are my questions about the above excersise:
- What is the meaning of
smallest set of languages that contains all the "basic" languages $\varnothing$,$\{\Lambda\}$, and $\{\sigma\}$ (for every $\sigma \in \Sigma$)
In other words, What are the sets that I should find for the answers?
- The solution manual suggested "Every zero or one member subset of $\{x | x\in\Sigma^*\}$" for closure under concatenation
I don't understand why it is closed under union? suppose $\{\sigma_1\}$. Is $\sigma_1\sigma_1$ closed under that? No.