Update Sat Mar 16 04:09:43 UTC 2024

Author: hrmacbeth

Math2001/Homework/hw6.lean

@@ -0,0 +1,44 @@
+/- Copyright (c) Heather Macbeth, 2023.  All rights reserved. -/
+import Mathlib.Data.Real.Basic
+import Library.Basic
+import Library.Tactic.ModEq
+import AutograderLib
+
+math2001_init
+set_option pp.funBinderTypes true
+
+/-! # Homework 6
+
+Don't forget to compare with the text version,
+https://github.com/hrmacbeth/math2001/wiki/Homework-6,
+for clearer statements and any special instructions. -/
+
+
+@[autograded 4]
+theorem problem1 (P Q : Prop) : (P ∨ Q) ↔ (Q ∨ P) := by
+  sorry
+
+@[autograded 5]
+theorem problem2 (P : α → Prop) (Q : Prop) : ((∃ x, P x) ∧ Q) ↔ ∃ x, (P x ∧ Q) := by
+  sorry
+
+@[autograded 5]
+theorem problem3 (P Q : Prop) : ¬ (P → Q) ↔ (P ∧ ¬ Q) := by
+  sorry
+
+@[autograded 3]
+theorem problem4 : ¬ (∀ x : ℝ, x ^ 2 ≥ x) := by
+  push_neg
+  sorry
+
+@[autograded 4]
+theorem problem5 : ¬ Int.Even 7 := by
+  dsimp [Int.Even]
+  push_neg
+  sorry
+
+@[autograded 4]
+theorem problem6 {p : ℕ} (k : ℕ) (hk1 : k ≠ 1) (hkp : k ≠ p) (hk : k ∣ p) : ¬ Prime p := by
+  dsimp [Prime]
+  push_neg
+  sorry