Need help with this question please

Has to be in LATEX

The declaration of the state of the system is defined by The set of phone numbers (call it numbers) that are recorded in contacts. A record of association between names and phone numbers, given by a correspondence (call it recorded). 1. Provide a diagram to visualize the state of the system. 2. Provide a formal definition for numbers. 3. Does recorded have to be captured by a function? What requirements would a function enforce? Explain in detail. 4. What is the domain and the codomain of recorded? 5. What type of function should recorded be (full or partial)? Explain in detail. 6. Will recorded be an injective, surjective, or bijective? Explain in detail. 7. Provide a formal definition for recorded. The declaration of the state of the system is defined by The set of phone numbers (call it numbers) that are recorded in contacts. A record of association between names and phone numbers, given by a correspondence (call it recorded). 1. Provide a diagram to visualize the state of the system. 2. Provide a formal definition for numbers. 3. Does recorded have to be captured by a function? What requirements would a function enforce? Explain in detail. 4. What is the domain and the codomain of recorded? 5. What type of function should recorded be (full or partial)? Explain in detail. 6. Will recorded be an injective, surjective, or bijective? Explain in detail. 7. Provide a formal definition for recorded