Problem 3: System Requirements and Satisfiability One way these logic foundations are helpful in practice is evaluating system requirements. When we start a project, we start from a list of requirements. Requirements vary in terms of whether they refer to overall system requirements, or the actual functioning of the system, or the experience of the user, or technical constraints. In this problem we're going to see how we can define some propositional formulas and use them to specify a system. We'll be looking at mobile devices. Specifically, when sound from either music or a game is played on a device's speaker (out loud) versus through headphones. We have the following propositions that describe the state of a mobile device: M: Music is being played. . G: A game is being played. H: Headphones are plugged into the device. D: Sound is being played on the device speaker (not in headphones). P: Sound is being played on the headphones (not on the device speaker). (a) Below are a number of statements using the propositions above. For each, write an interpretation of the statement. If any are ambiguous, note that and provide all interpretations (this is not intentional). i. D + (MVG) (2 ii. HAM + D iii. D+HA(MAG) iv. HAG +D v. H +D . (b) Below is a set of requirements based on the above-defined propositions. If no music or games are being played, then there is no sound coming from the headphones or device. If the headphones are plugged in, no sound plays on the device. If the headphones are plugged in and music or a game is being played, then sound is coming through the headphones. If music or a game is being played, then sound is coming from the headphones or device. i. Write out a set of propositional statements that reflect the above specifications/requirements. ii. Show these requirements are satisfiable by providing a set of truth values for each proposition that satisfies all requirements