1. Prove or disprove: Every finite belief space has a consistent belief subspace.
2. Prove or disprove: If Y˜ i(ω) is inconsistent for some player i ∈ N, then Y˜ (ω) is also inconsistent.
3. Prove or disprove: If Y˜ i(ω) is inconsistent for every player i ∈ N, then Y˜ (ω) is also inconsistent.