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Assignment 3

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# File week-02/assignment-03.markdown

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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.`