1. **Problem Statement:** Construct a regular expression (RE) for the language over the alphabet $\Sigma = \{0,1\}$ that accepts all strings starting with $1$ and ending with $00$. 2. **Understanding the problem:** The strings must start with the symbol $1$ and end with the substring $00$. Between the starting $1$ and ending $00$, any combination of $0$s and $1$s (including the empty string) is allowed. 3. **Formula and rules:** - The string starts with $1$. - The string ends with $00$. - The middle part can be any string over $\{0,1\}$, including empty. 4. **Constructing the RE:** - Start: $1$ - Middle: $(0|1)^*$ (zero or more occurrences of $0$ or $1$) - End: $00$ 5. **Final regular expression:** $$1(0|1)^*00$$ This RE matches all strings that start with $1$, end with $00$, and have any combination of $0$s and $1$s in between. **Example strings accepted:** $100$, $1100$, $10100$, $11100$, etc. **Example strings rejected:** $00$, $10$, $1$, $01100$ (does not start with $1$), $1001$ (does not end with $00$).