Anirudh Rao rao107
rao107
/ Ch1-5Q1.lean
Created
November 17, 2023 05:47
Chapter 1 Section 5 Q1 of Introduction to Topology by Mendelson
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| /- | |
| The original problem is incorrect. Instead, we prove that the statement is true | |
| if and only if either A or B is the universe | |
| -/ | |
| example (h0 : X ⊆ A) (h1 : Y ⊆ B) : | |
| A = Set.univ ∨ B = Set.univ ↔ (X ×ˢ Y)ᶜ = A ×ˢ Yᶜ ∪ Xᶜ ×ˢ B := by | |
| apply Iff.intro | |
| { | |
| intro h2 | |
| rw [Set.compl_prod_eq_union, Set.union_comm] |
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| def riddler_classic(): | |
| max_prob = 0 | |
| max_n = 0 | |
| for n in range(11, 100): | |
| prob = 1 | |
| for i in range(0, 8): | |
| prob *= (n - i) / (2 * n - i) | |
| for i in range(0, 11): | |
| prob *= (n - i) / (2 * n - 8 - i) |