## WEEK 1 :: Homework

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.