Using the MIU-system (see instructions) complete the following.
M1. Derive the theorem MUI.
M2. Derive the theorem MUUII.
M3. Is MUIIU a theorem? If so, derive it.
M4. Is MUUIU a theorem? If so, is there a shorter derivation of it than the shortest derivation of MUIIU?
M5. Is MU a theorem? If so, derive it; if not explain why.