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Steve Losh  committed 76e3ebb

Assignment 3

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+Assignment 2
+============
+
+Problems
+--------
+
+### Problem 1
+
+1. `T ⇒ (D ∧ Y)`
+2. `T ⇒ (Y ⇒ ¬D)`
+3. `T ∧ (T ⇒ ((D ∧ Y) ∨ (¬D ∧ ¬Y)))`
+
+### Problem 2
+
+    φ   ¬φ   ψ   (φ ⇒ ψ)   (¬φ ∨ ψ)
+    -------------------------------
+    T    F   T   T         T
+    T    F   F   F         F
+    F    T   T   T         T
+    F    T   F   T         T
+
+### Problem 3
+
+That `φ ⇒ ψ` and `¬φ ∨ ψ` are logically equivalent.
+
+This makes sense, because the implication is always true if φ is false.
+Otherwise it's only true when ψ is true.  Which is exactly what `¬φ ∨ ψ` says.
+
+### Problem 4
+
+    φ   ψ   ¬ψ    (φ ⇒ ψ)   (φ ⇏ ψ)   (φ ∧ ¬ψ)
+    ------------------------------------------
+    T   T   F     T         F         F
+    T   F   T     F         T         T
+    F   T   F     T         F         F
+    F   F   T     T         F         F
+
+### Problem 5
+
+That `(φ ⇏ ψ)` and `(φ ∧ ¬ψ)` are logically equivalent.
+
+This makes sense, because the only way for φ to "not imply" ψ is for φ to be
+true but ψ be false, which is exactly what `(φ ∧ ¬ψ)` says.