Question: 1. Let ∼ be an equivalence relation on a set S. Using the definition of equivalence class, prove that [a]=[b] if and only if a ∼ b.
2. You hang a 3×3×3 cube of pressed birdseed outside your window in order to attract avian wildlife. A grackle comes every day and eats a 1 × 1 × 1 cubelet of birdseed. You wonder can it eat the entire cube of birdseed by always eating a cubelet adjacent to the cubelet it ate the previous day?