If is a weak order on X, then for every y X, 1 (y) (y) X and (y) (y) Iy 2 (y) (y) X and (y) (y) 3 (y), Iy and (y) together partition X

Question: If is a weak order on X, then for every y X, 1. (y) (y) = X and (y) (y) =

If ≿ is a weak order on X, then for every y ∈ X,
1. ≿(y) ∪ ≾(y) = X and ≿(y) ∩ ≾(y) = Iy
2. ≿(y) ∪ (y) = X and ≿(y) ∩ ≺(y) = ϕ
3. ≻(y), Iy and ≺(y) together partition X

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